# Algebra 1 : Factoring Polynomials

## 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: 1 2 3 4 5 6 7 8 9 11 Next →

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