PSAT Math : How to find the value of the coefficient

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : 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 .

Example Question #23 : Polynomials

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 #24 : Polynomials

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 #2 : 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 #5 : 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.

Example Question #2 : 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 .

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