Answers
Answer:
[tex]y=2x^2+8x+11[/tex]Explanation:
A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
Given the coordinate (-2, 3), we'll have that;
h = -2
k = 3
Given a y-intercept of 11 and we know that at the y-intercept x = 0.
Substituting the above values into the vertex form equation and solving for a, we'll have;
[tex]\begin{gathered} 11=a\lbrack0-(-2)\rbrack^2+3 \\ 11=4a+3 \\ 4a=8 \\ a=\frac{8}{4} \\ a=2 \end{gathered}[/tex]Substituting a = 2, h = -2 and k = 3 into the vertex form equation and taking it to standard form, we'll have;
[tex]\begin{gathered} y=2(x+2)^2+3 \\ y=2(x^2+4x+4)+3 \\ y=2x^2+8x+8+3 \\ y=2x^2+8x+11 \end{gathered}[/tex]Related Questions
Jamal works as a computer network technician and last year they paid $4061 in social security tax. what was their annual income last year? Take the tax percentage as 6.2%
Answers
We know that Jamal paid 4061 of taxes and
[tex]4061=P\cdot(0.062)[/tex]where P is Jamal's income and 6.2% correspond to 0.062. Now, we must isolate P. It yields,
[tex]\begin{gathered} P=\frac{4061}{0.062} \\ P=65500 \end{gathered}[/tex]this means that Jamal's income was $65500 last year
Geometry question - Given: AB and AC are the legs of isosceles triangle ABC, measure of angle 1 = 5x, measure of angle three = 2x + 12. Find measure of angle 2 (reference picture)
Answers
Since triangle, ABC is an isosceles triangle because AB = BC
Then the angles of its base are equal
Since the angles of its bases are <2 and <4, then
[tex]m\angle2=m\angle4[/tex]Since <3 and <4 are vertically opposite angles
Since the vertically opposite angles are equal in measures, then
[tex]m\angle3=m\angle4[/tex]Since measure of <3 = 2x + 12, them
[tex]m\angle4=m\angle2=2x+12[/tex]Since <1 and <2 are linear angles
Since the sum of the measures of the linear angles is 180 degrees, then
[tex]m\angle2+m\angle1=180[/tex]Since m<1 = 5x, then
[tex]\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Then substitute x by 24 in the measure of <2
[tex]\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}[/tex]The measure of angle 2 is 60 degrees
Find the area of the sector of a circle with diameter 30 feet and an angle of 3Pi/5 radians. Round your answer to four decimal places.
Answers
half the diameter is the radius, so
[tex]r=15[/tex]now we can calculate the total area of the circle , and then will calculate the area for the angle
[tex]\begin{gathered} A=\pi\times r^2 \\ A=\pi\times15^2 \\ A=225\pi \end{gathered}[/tex]the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi
now we create a relation to find the area corresponding to the indicated angle
if 225pi is equal to 2pi how much is 3pi / 5
[tex]\begin{gathered} 225\pi\longrightarrow2\pi \\ x\longrightarrow\frac{3}{5}\pi \end{gathered}[/tex]where x is the area covered by the angle
we solve ussing cross multiplication, x is equal to: multiply the values that are found diagonally and make them equal
[tex]\begin{gathered} x\times2\pi=\frac{3}{5}\pi\times225\pi \\ \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=\frac{\frac{3}{5}\pi\times225\pi}{2\pi} \\ \\ x=\frac{135\pi^2}{2\pi} \\ \\ x=67.5\pi\approx212.0575 \end{gathered}[/tex]The rounded area is 212.0575 square feet
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
Answers
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
Let
x -----> first number
y -----> another number
we have that
3x+y=34 -------> equation A
5x-y=38 -----> equation B
solve by elimination
Adds the equations
so
8x=72
x=72/8
x=9
substitute
3(9)+y=34
y=34-27
y=7
therefore
the numbers are 9 and 7A. Step 1 B. Step 2 C. Omar did not make a mistake
Answers
To find out if Omar made a mistake, we must solve the equation step by step.
Step 1
[tex]\begin{gathered} 3x=4.5 \\ \text{divide through by 3} \\ \frac{3x}{3}=\frac{4.5}{3} \end{gathered}[/tex]Step 2
Simplify the final part in step 1
[tex]\begin{gathered} \frac{3x}{3}=\frac{4.5}{3} \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]Since, we have gone through all the steps and gotten exactly the same steps and solution as Omar, we can conclude that Omar did not make a mistake.
LEO AND OLIVER HAVE TLO CLEAN THIER BEDROOMS. OLIVER CLEANS HIS ROOM IN 3/4 OF AN HOUR.LEO TAKES TWICE AS LONG AS OLIVER. HOW DID IT TAKE LEO TO CLEAN HIS ROOM?
Answers
It took 1.5 hour for Leo to clean the room .
In the question ,
it is given that
Leo and Oliver clean their their room
time taken by Oliver to clean the room is = 3/4 of an hour = 0.75 hours .
and also given that Leo takes twice as long as Oliver
which means
time taken by Leo to clean the room = 2*(time taken by Oliver to clean the room )
On substituting the values
we get ,
time taken by Leo to clean the room = 2*(0.75 hours)
= 1.5 hours
Therefore , Leo takes 1.5 hours to clean the room .
Learn more about Equations here
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Given the figure above, determine the angle that is an alternate interior angle with respect to
Answers
Explanation
When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
so, the angle is
[tex]\measuredangle3[/tex]I hope this helps you
(2n^3+15n^2+11n-42)÷(n+6)
Answers
we have the following:
Question 2(Multiple Choice Worth 1 points)(07.02 MC)Factor completely x³ + 4x² + 8x + 32.O(x + 4)(x² + 8)O(x-4)(x²-8)O(x-4)(x² + 8)○ (x + 4)(x² − 8)
Answers
Given -
x³ + 4x² + 8x + 32
To Find -
Factor completely =?
Step-by-Step Explanation -
x³ + 4x² + 8x + 32 can be written as:
= (x³ + 4x²) + 8x + 32
= x²(x + 4) + 8(x + 4)
Now it can be written as:
(x² +8)(x + 4)
So, the complete factor of x³ + 4x² + 8x + 32 is (x + 4)(x² + 8)
Final Answer -
A. (x+4)(x² + 8)
Given ST is tangent to circle Q, find the value of r
Answers
Given the figure of the circle Q
As shown, ST is tangent to circle Q
So, ST is perpendicular to the radius QS
So, the triangle QST is a right-angle triangle
We can apply the Pythagorean theorem where the legs are QS and ST
And the hypotenuse is QT
The side lengths of the triangle are as follows:
QS = r
ST = 48
QT = r + 36
So, we can write the following equation:
[tex]\begin{gathered} QT^2=QS^2+ST^2 \\ (r+36)^2=r^2+48^2 \end{gathered}[/tex]Expand then simplify the last expression:
[tex]\begin{gathered} r^2+2*36r+36^2=r^2+48^2 \\ r^2+72r+1296=r^2+2304 \end{gathered}[/tex]Combine the like terms then solve for (r):
[tex]\begin{gathered} r^2+72r-r^2=2304-1296 \\ 72r=1008 \\ \\ r=\frac{1008}{72}=14 \end{gathered}[/tex]So, the answer will be r = 14
Which choices are equations for the line shown below? Check all that apply.(-2,5) 51(2-3)A. y + 3 = -2(x-2)B. y-5= -2(x + 2)O C. y = 2x + 1I D. y=-0.5x + 1E. y-5--2(x-2)OF. y=-2x + 1
Answers
Solution
For this case we have two points given :
(-2,5) and (2,-3)
We can find the slope on this way:
[tex]m=\frac{-3-5}{2-(-2)}=-2[/tex]And the intercept would be:
5 = -2(-2)+b
5 = 4 +b
b= 1
Then the original equation is:
y= -2x+1
And we need to find equivalent equations so we can analyze one by one the options like this:
A. y+3 = -2(x-2)
y+3 = -2x+4
y =-2x+1
B. y-5 = -2(x+2)
y-5 =-2x-4
y = -2x +1
C. y=2x+1
D. y= -0.5x +1
E. y-5 = -2(x-2)
y-5 = -2x +4
y= -2x+9
Then the correct options are A and B
what do 13% and 0.125 and 1/5 and 10 % have in common
Answers
Comparing 13%, 0.125 , 1/ 5 and 10%
1. 13 % = 0.13
2. 0.125 = 0.13 ( 2 decimal places)
3. 1/5 = 0.2
4. 10 % = 0.1
Conclusion : 13% and 0.125 have things in common
A binomial experiment consists of 18 trials. The probability of success on trial 11 is 0.79. What is theprobability of success on trial 15?0.790.280.610.460.560.72
Answers
Answer:
0.79
Explanation:
Given a binomial experiment with 18 trials; and
[tex]P(\text{ success on trial 11\rparen}=0.79[/tex]By the conditions required for a binomial experiment, the probability of success (or failure) remains the same throughout the experiment and for each and every trial.
Therefore:
[tex]P(\text{ success on trial 15\rparen}=0.79[/tex]The answer is 0.79
hello, please help me solve to find the correct polynomials!
Answers
INFORMATION:
We have the next polynomials
And we must factor them to complete the next table
STEP BY STEP EXPLANATION:
1.
[tex]x^2-8x+15[/tex]To factor it, we must look for two number that multiplied be equal to 15 and added up be equal to -8.
These two numbers would be -5 and -3.
- -5 x -3 = 15
- -5 - 3 = -8
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} x^2-8x+15=(x-5)(x-3) \\ \text{ So, }a=1,b=-5,c=1,d=-3 \end{gathered}[/tex]2.
[tex]2x^3-8x^2-24x[/tex]To factor it, we must first take the common factor 2x from the expression
[tex]2x(x^2-4x-12)[/tex]Now, we must factor the terms in the parenthesis. We must look for two number that multiplied be equal to -12 and added up be equal to -4. These two numbers would be -6 and 2.
- -6 x 2 = -12
- -6 + 2 = -4
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} 2x(x+2)(x-6) \\ \text{ So, }a=1,b=2,c=1,d=-6 \end{gathered}[/tex]3.
[tex]6x^2+14x+4[/tex]To factor it, we must first take the common factor 2 from the expression
[tex]2(3x^2+7x+2)[/tex]Then, we divide the 7x term in the parenthesis in two terms
[tex]2(3x^2+6x+x+2)[/tex]Now, we can take the common factor x + 2 in the parenthesis
[tex]2(3x(x+2)+(x+2))[/tex]Finally, we can take the common factor x + 2 in the complete expression
[tex]\begin{gathered} 2(x+2)(3x+1) \\ \text{ Simplifying,} \\ =\left(3x+1\right)(2x+4) \\ \text{ So, }a=3,b=1,c=2,d=4 \end{gathered}[/tex]ANSWER:
what is 80% of 685?
Answers
548
1) To find what is 80% of 685 we need to rewrite that percentage as a decimal number
[tex]80\%=0.8[/tex]2) So, to find what is 80% we need to multiply 0.8 by 685
[tex]0.8\times685=548[/tex]Thus, 548 is 80% of 685
1.Orange paint uses 3 parts yellow to 2 parts red.The equation y=3/5t can be used to find the cups of yellow paint when given the total cups of paint.Use the equation to complete the table.t. 0 5 10 15 20 25 y _ _ _ _ _ _2.plot the point in the column in the table in problem 1.Then draw a line to represent the equation.3.The equation r=2/5t can be used to find the cups of red paint when given the total cups of paint.Draw a line represent the equation.
Answers
we have the equation
y=(3/5)t
so
Find the values of y for different valyes of t
For t=0
y=(3/5)(0)
y=0
For t=5
y=(3/5)(5)
y=3
For t=10
y=(3/5)(10)
y=6
For t=15
y=(3/5)(15)
y=9
For t=20
y=(3/5)(20)
y=12
For t=25
y=(3/5)(25)
y=15
A boat sails directly away from a skyscraper located on the edge of a large lake. The skyscraper is 120 meters tall. A photographer on the boat is taking pictures of the skyscraper with a camera that has a 28° viewing lens.
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} Height(h)=120m \\ \theta=28^{\circ} \\ d=\text{?} \end{gathered}[/tex]We will use the Trigonometric ratio (SOHCAHTOA) to solve for d. In this case, we will use ''TOA''
[tex]\begin{gathered} TOA\Rightarrow tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \\ opposite\Rightarrow height=120m \\ adjacent\Rightarrow d \\ \theta=28^{\circ} \\ tan28^{\circ}=\frac{120}{d} \\ d\cdot tan28^{\circ}=120 \\ d=\frac{120}{tan28^{\circ}}=225.687\approx226 \\ d=226m \end{gathered}[/tex]What is the solution to -4y=28 please explain
Answers
You have the equation -4y=28
To solve this equation you need to clear the value of the unknown variable y, meaning, you have to simplfy the equation until you reach y=
For this, since y is multiplied by -4 you have to divide it by -4 to leave y alone, and what you do in one side of the equation must be done to the other side to keep the equality:
[tex]\begin{gathered} -4y=28 \\ \frac{-4y}{-4}=\frac{28}{-4} \\ y=-7 \end{gathered}[/tex]The value of y=-7
Gordon works for a graphic design firm and is creating a label for a food truck vendor. The vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. To complete his label, Gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. Gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches.
Answers
Part A
Find out the slant height of the cone
Applying the Pythagorean Theorem
AC^2=AB^2+BC^2
we have
AC ----> slant height
AB=4/2=2 in
BC=6 in
substitute given values
AC^2=2^2+6^2
AC^2=40
AC=2√10 in
Part B
Find out the measure of the angle formed between the base and the slant height
we have that
tan( by opposite side divided by adjacent side
tan(mm
Part C
see the figure below to better understand the problem
we have that
AC and DC are slant height
triangle ADC is an isosceles triangle
because AC=DC
that means
mmmmthe answer part C is 36.86 degrees
Find the absolute change and the relative change in the following cases.The number of refugees in the world increased from 8.7 million in 2005 to 16.1 million in 2015.
Answers
absolute change is determined by the absolute value of the subtraction of the number of refugees in both years:
absolute change = | 16.1 million - 8.7 million | = 7.4 million
Relative change is given by the quotient between final value and initial value, just as follow:
relative change = final value / initial value
= 16.1 million / 8.7 million
= 1.85
Hence, the absolute change is 7.4 million and relative change is of 1.85
A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. Use 3.14 for pi and round answers to the nearest hundredth, if applicable.a.) What is the measure of each central angle between any two cars? (4 points)b.) What is the arc length of each sector between any two cars? (4 points)c.) What is the area of each sector between any two cars?
Answers
The carnival ride is in shape of wheel with 25ft radius.
The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the
the measure of the angle between each car by dividing 360 degrees by 20.
#A:
The measure of each central angle between any two cars is:
[tex]\frac{360}{20}=18^0[/tex]#B:
Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:
[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ \text{where,} \\ r=\text{radius} \\ \theta=\text{measure of each central angle betw}een\text{ two cars} \end{gathered}[/tex]Let us calculate this length below:
[tex]\begin{gathered} \theta=18^0 \\ \frac{18}{360}\times2\pi\times25 \\ =2.5\pi=7.85\text{ (to the nearest hundredth)} \end{gathered}[/tex]#C:
We are asked to find the area of each sector between two cars.
The area of a sector of a circle is:
[tex]\frac{\theta}{360}\times\pi\times r^2[/tex]Since we have all the parameters, let us calculate this area:
[tex]\begin{gathered} Area=\frac{18}{360}\times\pi\times25^2 \\ \\ Area=98.13\text{ (to nearest hundredth)} \end{gathered}[/tex]Therefore, the final answers are:
#A: angle = 18 degrees
#B length = 7.85 feet
#C Area = 98.13 squared feet
rewrite csc(theta) / sec(theta) as a single trig function with no fractions
Answers
The given expression is
[tex]\frac{\csc \theta}{\sec \theta}[/tex][tex]\text{ We know that }csc\theta=\frac{1}{\sin x}\text{ and }\sec \theta=\frac{1}{cos\theta}\text{.}[/tex]Using the reciprocal, we get
[tex]\frac{\csc\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}}{\frac{1}{\cos \theta}}[/tex][tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\frac{\csc\theta}{\sec\theta}=\frac{1}{\sin\theta}\times\frac{\cos \theta}{1}[/tex][tex]\text{ Use }\frac{\cos\theta}{\sin\theta}=\cot \theta.[/tex][tex]\frac{\csc\theta}{\sec\theta}=\cot \theta[/tex]Hence the answer is
[tex]\cot \theta[/tex]7. Find two consecutive even integers such that twice the smaller diminished by twenty is equal to thelarger.
Answers
Given two consecutive even integer numbers x and x + 2, we know that twice the smaller number diminished by twenty is equal to the larger:
[tex]2x-20=x+2[/tex]Solving for x:
[tex]\begin{gathered} 2x-x=20+2 \\ \\ \Rightarrow x=22 \end{gathered}[/tex]And the numbers are:
[tex]22\text{ and }24[/tex]There is a population of 2,363 bacteria in a colony. If the number of bacteria doubles every 157 minutes, what will the population be 314 minutes from now?
Answers
9452
Explanation
an exponential function is given by:
[tex]\begin{gathered} y=a(b)^x \\ \text{where a is the initial amount} \\ b\text{ is the rate of change} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Set the equations
a) initial population = 2363
time=0
replace
[tex]\begin{gathered} y=a(b)^x \\ 2363=a(b^0) \\ 2363=a\cdot1 \\ 2363=a \end{gathered}[/tex]b) If the number of bacteria doubles every 157 minutes
[tex]\begin{gathered} (2363\cdot2)=2363(b^{157}) \\ (2363\cdot2)=2363(b^{157}) \\ 4726=2363b^{157} \\ \text{divide both sides by }2363 \\ \frac{4726}{2363}=\frac{2363b^{157}}{2363} \\ 2=b^{157} \\ 2^{(\frac{1}{157})}=(b^{157})^{\frac{1}{157}} \\ 1.00442471045\text{ =b} \end{gathered}[/tex]so, the function is
[tex]y=2363(1.00442471045)^x[/tex]Step 2
what will the population be 314 minutes from now?
Let
time=x =314
replace
[tex]\begin{gathered} y=2363(1.00442471045)^x \\ y=2363(1.00442471045)^{314} \\ y=2363\cdot4 \\ y=9452 \end{gathered}[/tex]therefore, the answer is
9452
I hope this helps you
Mr. Smith took a job that the employment agency. The job pays $76k per year. The employment agency is charging a fee of 19% of his first 4 weeks' pay. How much money does Mr. Smith give to the agency.
Answers
Answer:
Mr. Smith gave $1110.7 to the agency
Explanation:
Given that the job Mr. Smith took pays $76k per year.
In his first 4 weeks, taking the number of weeks per year to be 52, he is paid:
4 × ($76000)/52
= 4 × $1461.5 (Approximately)
= $5846
He is charged 19% of this earnings:
19% of $5846 is:
0.19 × $5846
= $1110.7
What he has in the end is:
$17000 - $1110.7
= $15889.3
A triangle on a coordinate plane is translated according to the rule T-3,5(X,Y) what is another way to write this ?
Answers
Given the translation rule as :
[tex]T_{-3,5}(x,y)[/tex]Solution
Another way of writing this is:
[tex](x,\text{ y) }\rightarrow\text{ (}x\text{ - 3, y + 5)}[/tex]This means that the original coordinates (x,y) would be translated 3 units to the left and 5 units upwards to give the new coordinates.
Answer: Option A
Use the ordered pairs (3,56) and (7,85) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. If necessary round the slope to the nearest hundredth and the y intercept to the nearest whole number
Answers
Equation of a line in slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ \\ m\colon\text{slope} \\ b\colon y-\text{intercept} \end{gathered}[/tex]1. Find the slope: Use two ordered pairs (x,y) in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Ordered pairs (3,56) and (7,85)} \\ m=\frac{85-56}{7-3}=\frac{29}{4}=7.25 \end{gathered}[/tex]Slope: m=7.25
2. Find the y-interept: Use one ordered pair and the slope to find b:
[tex]\begin{gathered} \text{ordered pair: (3,56)} \\ x=3 \\ y=56 \\ \\ \text{Slope: m=7.25}_{} \\ \\ y=mx+b \\ 56=7.25(3)+b \\ 56=21.75+b \\ 56-21.75=b \\ \\ b=34.25 \\ \\ b\approx34 \end{gathered}[/tex]y-intercept: b= 34
Then, the equation of the line is:[tex]y=7.25x+34[/tex]20.Dilate Point B by a scale factor of 1/2Va) (1.5,-4)c) (-1,-1.5)b) (-1.5,1)d) (-2,-2)
Answers
the coordinate of point B is (-3,2)
In order to dilate the point with a scale factor of 1/2 we need to multiplicate the scale factor by the coordinate-x and the coordinate-y
coordinate x
[tex]-3\cdot\frac{1}{2}=-1.5[/tex]coordinate y
[tex]2\cdot\frac{1}{2}=1[/tex]the coordinate dilate is
B'(-1.5,1)
the correct answer is b
what is the slope of a line perpendicular to y=-3/4x-1
Answers
As given by the question
There are given that the equation
[tex]y=-\frac{3}{4}x-1[/tex]Now,
For find the slope of line perpendicular to given equation
The formula is:
[tex]m_{perpendicular}=-\frac{1}{m}[/tex]Here,
From the equation, the value of m is,
[tex]m=-\frac{3}{4}[/tex]Then,
Put the value of m into the above formula
So,
[tex]\begin{gathered} m_{perpendicular}=-\frac{1}{m} \\ m_{perpendicular}=-\frac{1}{-\frac{3}{4}} \\ m_{perpendicular}=\frac{4}{3} \end{gathered}[/tex]Hence, the correct option is C
Factor the given trinomial. If the trinomial cannot be factored, indicate “not factorable” 6v^5-18v^4-168v^3
Answers
The polynomial is given below as
[tex]6v^5-18v^4-168v^3[/tex]Step 1: Factor out the highest common factor which is
[tex]6v^3[/tex][tex]\begin{gathered} 6v^5-18v^4-168v^3=6v^3(\frac{6v^5}{6v^3}-\frac{18v^4}{6v^3}-\frac{168v^3}{6v^3}) \\ 6v^5-18v^4-168v^3=6v^3(v^2-3v-28) \end{gathered}[/tex]Step 2: Factorise the quadratic expression
[tex]v^2-3v-28[/tex]To factorize the quadratic expression, we will have to look for two factors that will multiply each other to give a -28, and then the same two factors will add up together to give -3
By try and error, we will have the two factors to be
[tex]\begin{gathered} -7\times+4=-28 \\ -7+4=-3 \end{gathered}[/tex]By replacing the two factors in the equation above, we will have
[tex]\begin{gathered} v^2-3v-28=v^2-7v+4v-28 \\ \text{group the factors to have} \\ (v^2-7v)+(4v-28)=v(v-7)+4(v-7) \\ v^2-3v-28=(v-7)(v+4) \end{gathered}[/tex]Hence,
[tex]6v^5-18v^4-168v^3=6v^3(v-7)(v+4)[/tex]Therefore,
The final answer is 6v³(v - 7)(v + 4)