### All GED Math Resources

## Example Questions

### Example Question #1 : Simplifying, Distributing, And Factoring

Multiply:

**Possible Answers:**

**Correct answer:**

### Example Question #2 : Simplifying, Distributing, And Factoring

Factor:

**Possible Answers:**

**Correct answer:**

where

The numbers and fit those criteria. Therefore,

You can double check the answer using the FOIL method

### Example Question #3 : Simplifying, Distributing, And Factoring

Which of the following is *not* a prime factor of ?

**Possible Answers:**

**Correct answer:**

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 #4 : Simplifying, Distributing, And Factoring

Which of the following is a prime factor of ?

**Possible Answers:**

**Correct answer:**

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 #5 : Simplifying, Distributing, And Factoring

Divide:

**Possible Answers:**

**Correct answer:**

Divide termwise:

### Example Question #6 : Simplifying, Distributing, And Factoring

Multiply:

**Possible Answers:**

**Correct answer:**

This product fits the difference of cubes pattern, where :

so

### Example Question #1 : Simplifying, Distributing, And Factoring

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

**Possible Answers:**

**Correct answer:**

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 #8 : Simplifying, Distributing, And Factoring

Which of the following is a factor of the polynomial ?

**Possible Answers:**

**Correct answer:**

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:**

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 #10 : Simplifying, Distributing, And Factoring

Which of the following is a factor of the polynomial

**Possible Answers:**

**Correct answer:**

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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