GED Math : Simplifying, Distributing, and Factoring

Example Questions

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Multiply:

Explanation:

Example Question #2 : Simplifying, Distributing, And Factoring

Factor:

Explanation:

where

The numbers and fit those criteria. Therefore,

You can double check the answer using the FOIL method

Example Question #2 : Algebra

Which of the following is not a prime factor of  ?

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  ?

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.

Divide:

Explanation:

Divide termwise:

Example Question #1 : Algebra

Multiply:

Explanation:

This product fits the difference of cubes pattern, where :

so

Example Question #7 : Simplifying, Distributing, And Factoring

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

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 #4 : Algebra

Which of the following is a factor of the polynomial  ?

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 #5 : Algebra

Which of the following is a prime factor of  ?

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 : Algebra

Which of the following is a factor of the polynomial

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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