Algebra 1 : Factoring Polynomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #411 : Polynomials

Factor the following polynomial: .

Possible Answers:

Correct answer:

Explanation:

Because the term doesn’t have a coefficient, you want to begin by looking at the  term () of the polynomial: .  Find the factors of  that when added together equal the second coefficient (the term) of the polynomial. 

There are only four factors of : , and only two of those factors, , can be manipulated to equal  when added together and manipulated to equal  when multiplied together: (i.e.,). 

Example Question #101 : Factoring Polynomials

Factor the following polynomial: .

Possible Answers:

Correct answer:

Explanation:

Because the  term doesn’t have a coefficient, you want to begin by looking at the  term () of the polynomial: 

Find the factors of  that when added together equal the second coefficient (the  term) of the polynomial:

There are seven factors of , and only two of those factors, , can be manipulated to equal  when added together and manipulated to equal  when multiplied together:  

Example Question #11 : How To Factor A Variable

Solve for  when 

Possible Answers:

Correct answer:

Explanation:

First, factor the numerator: .  

Now your expression looks like 

Second, cancel the "like" terms -  - which leaves us with .  

Third, solve for , which leaves you with 

Example Question #11 : How To Factor A Variable

Factor the following polynomial: .

Possible Answers:

Correct answer:

Explanation:

Because the  term has a coefficient, you begin by multiplying the  and the  terms () together: 

Find the factors of  that when added together equal the second coefficient (the  term) of the polynomial: 

There are four factors of , and only two of those factors, , can be manipulated to equal  when added together and manipulated to equal  when multiplied together:  

Example Question #422 : Polynomials

Factor:  

Possible Answers:

Correct answer:

Explanation:

For each term in this expression, we will notice that each shares a variable of .  This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:  

Example Question #11 : How To Factor A Variable

Factor:  

Possible Answers:

Correct answer:

Explanation:

For each term in this expression, we will notice that each shares a variable of .  This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:  

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