What if you had a quadratic expression like

### Watch This

CK-12 Foundation: 0908S Factoring Quadratic Expressions

### Guidance

**Quadratic polynomials** are polynomials of the

where **trinomials**, since they are polynomials with three terms.)

You’ve already learned how to factor quadratic polynomials where

**Factor when a = 1, b is Positive, and c is Positive**

First, let’s consider the case where

You know from multiplying binomials that when you multiply two factors

Then we simplify by combining the like terms in the middle. We get:

So to factor a quadratic, we just need to do this process in reverse.

This means that we need to find two numbers

The factors of

such that

#### Example A

*Factor*

**Solution**

We are looking for an answer that is a product of two binomials in parentheses:

We want two numbers

So the answer is

We can check to see if this is correct by multiplying

The answer checks out.

#### Example B

*Factor*

**Solution**

We are looking for an answer that is a product of two binomials in parentheses:

The number 12 can be written as the product of the following numbers:

The answer is

#### Example C

*Factor*

**Solution**

We are looking for an answer that is a product of two binomials in parentheses:

The number 12 can be written as the product of the following numbers:

The answer is

Watch this video for help with the Examples above.

CK-12 Foundation: Factoring Quadratic Expressions

### Guided Practice

*Factor*

**Solution**

We are looking for an answer that is a product of two binomials in parentheses:

The number 36 can be written as the product of the following numbers:

The answer is

### Explore More

Factor the following quadratic polynomials.

x2+10x+9 x2+15x+50 x2+10x+21 x2+16x+48 - \begin{align*}x^2+14x+45\end{align*}
- \begin{align*}x^2+15x+50\end{align*}
- \begin{align*}x^2+22x+40\end{align*}
- \begin{align*}x^2+15x+56\end{align*}
- \begin{align*}x^2+2x+1\end{align*}
- \begin{align*}x^2+10x+24\end{align*}
- \begin{align*}x^2+17x+72\end{align*}
- \begin{align*}x^2+25x+150\end{align*}

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.8.