ACT Math : How to find the value of the coefficient

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Find The Value Of The Coefficient

What is the value of the coefficient in front of the term that includes in the expansion of ?

 

Possible Answers:

Correct answer:

Explanation:

Using the binomial theorem, the term containing the x2 ywill be equal to

 Act_math_113_14(2x)2(–y)7

=36(–4x2 y7)= -144x2y7

Example Question #2 : How To Find The Value Of The Coefficient

A function of the form  passes through the points  and .  What is the value of  ?

Possible Answers:

Correct answer:

Explanation:

The easisest way to solve for  is to begin by plugging each pair of coordinates into the function.

Using our first point, we will plug in  for  and  for .  This gives us the equation

.

Squaring 0 gives us 0, and multiplying this by  still gives 0, leaving only  on the right side, such that

.

We now know the value of , and we can use this to help us find .  Substituting our second set of coordinates into the function, we get

 which simplifies to

.

However, since we know , we can substitute to get

subtracting 7 from both sides gives

and dividing by 4 gives our answer

.

Example Question #2 : How To Find The Value Of The Coefficient

 is equivalent to which of the following?

Possible Answers:

Correct answer:

Explanation:

To answer this problem, we need to multiply the expressions together, being mindful of how to correctly multiply like variables with exponents. To do this, we add the exponents together if the the like variables are being multiplied and subtract the exponents if the variables are being divided. So, for the presented data:

We then multiply the remaining expressions together. When we do this, we will multiply the coefficients together and combine the different variables into the final expression. Therefore:

This means our answer is .

Example Question #284 : Polynomials

Give the coefficient of  in the product  

.

Possible Answers:

Correct answer:

Explanation:

While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two  terms and one constant are multiplied; find the three products and add them, as follows:

 

 

 

 

Add: .

The correct response is .

Example Question #40 : Variables

Give the coefficient of  in the product  

Possible Answers:

Correct answer:

Explanation:

While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two  terms and one constant are multiplied; find the three products and add them, as follows:

 

 

 

Add: 

The correct response is .

Example Question #3 : How To Find The Value Of The Coefficient

Give the coefficient of  in the binomial expansion of .

Possible Answers:

Correct answer:

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is 

Therefore, the  coefficient can be determined by setting 

:

Example Question #4 : Coefficients

Give the coefficient of  in the binomial expansion of .

Possible Answers:

Correct answer:

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is 

Therefore, the  coefficient can be determined by setting 

:

Example Question #5 : Coefficients

Give the coefficient of  in the binomial expansion of .

Possible Answers:

Correct answer:

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is 

Therefore, the  coefficient can be determined by setting 

Example Question #4 : How To Find The Value Of The Coefficient

Give the coefficient of  in the product

.

Possible Answers:

Correct answer:

Explanation:

While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two  terms and one constant are multiplied; find the three products and add them, as follows:

 

 

 

Add: 

The correct response is -122.

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: