GED Math : Simplifying, Distributing, and Factoring

Study concepts, example questions & explanations for GED Math

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Example Questions

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Example Question #1 : Simplifying, Distributing, And Factoring

Multiply:

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : Simplifying, Distributing, And Factoring

Factor:

Possible Answers:

Correct answer:

Explanation:

where

The numbers and fit those criteria. Therefore,

You can double check the answer using the FOIL method

Example Question #2 : Simplifying, Distributing, And Factoring

Which of the following is not a prime factor of  ?

Possible Answers:

Correct answer:

Explanation:

Factor  all the way to its prime factorization.

 can be factored as the difference of two perfect square terms as follows:

 is a factor, and, as the sum of squares, it is a prime.  is also a factor, but it is not a prime factor - it can be factored as the difference of two perfect square terms. We continue:

Therefore, all of the given polynomials are factors of , but  is the correct choice, as it is not a prime factor.

Example Question #1 : Algebra

Which of the following is a prime factor of  ?

Possible Answers:

Correct answer:

Explanation:

 can be seen to fit the pattern 

:

where 

 can be factored as , so

 .

 does  not fit into any factorization pattern, so it is prime, and the above is the complete factorization of the polynomial. Therefore,  is the correct choice.

Example Question #3 : Simplifying, Distributing, And Factoring

Divide: 

 

Possible Answers:

Correct answer:

Explanation:

Divide termwise:

Example Question #6 : Simplifying, Distributing, And Factoring

Multiply:

Possible Answers:

Correct answer:

Explanation:

This product fits the difference of cubes pattern, where :

so

Example Question #4 : Simplifying, Distributing, And Factoring

Give the value of  that makes the polynomial  the square of a linear binomial. 

Possible Answers:

Correct answer:

Explanation:

A quadratic trinomial is a perfect square if and only if takes the form

 for some values of  and .

, so 

 and 

For  to be a perfect square, it must hold that 

,

so . This is the correct choice.

Example Question #5 : Simplifying, Distributing, And Factoring

Which of the following is a factor of the polynomial  ?

Possible Answers:

Correct answer:

Explanation:

Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that  is a factor of polynomial  if and only if . We substitute 1, 2, 4, and 9 for  in the polynomial to identify the factor.

:

 

:

 

 

:

 

:

 

Only  makes the polynomial equal to 0, so among the choices, only  is a factor.

Example Question #9 : Simplifying, Distributing, And Factoring

Which of the following is a prime factor of  ? 

Possible Answers:

Correct answer:

Explanation:

 is the sum of two cubes:

As such, it can be factored using the pattern 

where ;

The first factor,as the sum of squares, is a prime.

We try to factor the second by noting that it is "quadratic-style" based on . and can be written as

;

we seek to factor it as 

 

We want a pair of integers whose product is 1 and whose sum is . These integers do not exist, so  is a prime. 

 

 is the prime factorization and the correct response is .

Example Question #6 : Simplifying, Distributing, And Factoring

Which of the following is a factor of the polynomial 

Possible Answers:

Correct answer:

Explanation:

Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that  is a factor of polynomial  if and only if . We substitute  and  for  in the polynomial to identify the factor.

 

:

 

:

 

:

 

:

 

Only  makes the polynomial equal to 0, so of the four choices, only  is a factor of the polynomial.

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