High School Math : Polynomials

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #4 : Factoring Polynomials

Factor this expression:

Possible Answers:

Correct answer:

Explanation:

First consider all the factors of 12:

1 and 12

2 and 6

3 and 4

Then consider which of these pairs adds up to 7.  This pair is 3 and 4.

Therefore the answer is .

Example Question #1 : Factoring Polynomials

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

This is a difference of perfect cubes so it factors to . Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the -axis. Therefore, your answer is only 1.

Example Question #2 : Factoring Polynomials

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Factor the equation to . Set  and get one of your 's to be . Then factor the second expression to . Set them equal to zero and you get

Example Question #5 : Factoring Polynomials

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting  from the polynomial:

Now, factor the remainder of the polynomial as a difference of cubes:

Example Question #6 : Factoring Polynomials

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by rearranging like terms:

Now, factor out like terms:

 

Rearrange the polynomial:

Example Question #7 : Factoring Polynomials

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by rearranging like terms:

 

Now, factor out like terms:

 

Rearrange the polynomial:

Factor:

Example Question #8 : Factoring Polynomials

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by separating  into like terms. You do this by multiplying  and , then finding factors which sum to 

Now, extract like terms:

Simplify:

Example Question #21 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To begin, distribute the squares:

 

Now, combine like terms:

Example Question #22 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting  from the polynomial:

 

Now, distribute the cubic polynomial:

Example Question #23 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting like terms:

 

Now, rearrange the right side of the polynomial by reversing the signs:

 

Combine like terms:

 

Factor the square and cubic polynomial:

Learning Tools by Varsity Tutors