# How do you determine whether x+2 is a factor of the polynomial #5x^2+2x+6#?

##### 2 Answers

You see if

#### Explanation:

Let's suppose you have this factorized polynomial:

A property of this factorized polynomial is that each of it's factors when set to 0 is the root to this polynomial.

For example, when

This property arises from the property in which when

Now, back to your polynomial. Let's set it to 0 first and solve for

Using the quadratic formula, we get

So,

Use the remainder theorem to find

#### Explanation:

**RemainderTheorem**

Given a polynomial

In our example:

#f(x) = 5x^2+2x+6#

and:

#f(-2) = 5(color(blue)(-2))^2+2(color(blue)(-2))+6#

#color(white)(f(-2)) = 20-4+6#

#color(white)(f(-2)) = 22#

Since this is not zero,