# Algebra 1 : How to factor a polynomial

## Example Questions

### Example Question #61 : Factoring Polynomials

Factor the polynomial.

Explanation:

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of -4 that add up to 3.

They are 4 and -1.

That gives you the answer .

### Example Question #61 : Factoring Polynomials

Factor the polynomial.

Explanation:

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of -3 that add up to 1.

They are 3 and -1.

That gives you the answer .

### Example Question #63 : How To Factor A Polynomial

Factor the polynomial.

Explanation:

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of -5 and factors of 2 that, when combined, add up to -9.

They are -5 and 1 and 2 and 1.

That gives you the answer .

### Example Question #64 : How To Factor A Polynomial

Factor the polynomial.

Explanation:

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of 12 that add up to 7.

They are 3 and 4.

That gives you the answer .

### Example Question #61 : Factoring Polynomials

Factor the polynomial.

Explanation:

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of 6 and factors of 3 that, when combined, add up to -11.

They are 3 and 2 and -1 and -3.

That gives you the answer .

### Example Question #66 : Factoring Polynomials

Factor the following polynomial

Explanation:

Factoring a polynomial is the reverse of distributing. What common factor exists for both  and ? We know that

and

So we can factor out  from the expression and get

Don't forget the negative sign!

### Example Question #62 : Factoring Polynomials

Factor

Explanation:

First, since there are no subtractive operations in the original expression, start by noting that all signs within the factors will be positive (i.e. (x + x)(x + x)).

Then, look at the highest degree variables.

We have .

The only possible ways to factor that are

and .

Then look at .

The only way to fact that is , so we know that 2x and x will appear in our final answer.

Write down .

Then, try inserting the possibilities we came up with for creating  into the blank spaces.

By trying the various permutations you should come up with the answer.

### Example Question #61 : How To Factor A Polynomial

Solve for :

Explanation:

The goal is to get x by itself on one side.

Start by getting all terms with x in them on the left side of the equation.

Add  to each side to get

.

Then, factor x out of the left side of the equation to get

.

Divide each side of the equation by  to solve for x and get the answer to the problem.

### Example Question #62 : Factoring Polynomials

Solve for :

Explanation:

Remember to read the question carefully.

It asks you to solve for h, not x.

So you can eliminate two answers right away.

Then, look to see if you can factor anything.

Factor x out of the right side of the equation to get

.

Divide both sides of the equation by x to get

.

Then, subtract  from each side and divide by  to get the answer!

### Example Question #66 : How To Factor A Polynomial

Factor

.

Explanation:

Start with the highest exponent. In two factors,  can only be made by multplying  and . Because everything in the original expression is positive, you know that all the factors in the answer also have to be positive.

Write down what you know if the form

.

Now, look at the term with the lowest exponent, 4. You can only make this with positive number by squaring 2 or multiplying 4 by 1. Then notice that the  term is multiplied by 4 and not 2. This means that 4 must be factored into 1 and 4 in our answer. Ths also means that the 4 must be in the factor with , because if it was in the factor with  they would never be multiplied together to create .

Try inserting 1 and 4 into the blank spaces of our previous expression. Foil the expression you created to check your answer.