High School Math : Factoring Polynomials

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Factoring Polynomials

Factor

Possible Answers:

Cannot be Factored

Correct answer:

Explanation:

Use the difference of perfect cubes equation:

In ,

 and

Example Question #2 : Factoring Polynomials

Factor the polynomial completely and solve for .

Possible Answers:

Correct answer:

Explanation:

To factor and solve for  in the equation 

Factor  out of the equation

Use the "difference of squares" technique to factor the parenthetical term, which provides the completely factored equation:

Any value that causes any one of the three terms , and  to be  will be a solution to the equation, therefore

Example Question #3 : Factoring Polynomials

Factor the following expression:

Possible Answers:

Correct answer:

Explanation:

You can see that each term in the equation has an "x", therefore by factoring "x" from each term you can get that the equation equals .

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 #269 : Algebra Ii

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 #1 : 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 #1 : 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:

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