If a polynomial has a root of −2, what FACTOR will divide evenly into the polynomial?

The factors of a polynomial divide the polynomial evenly, without remainder

The factor of the polynomial is x + 2

The root of the polynomial is given as:

Assume the polynomial is a function of x.

i.e. the variable of the polynomial is x

Then the root can be represented as:

Add 2 to both sides

So, we have:

Hence, the factor of the polynomial is x + 2

Read more about polynomial factors at:

link

Given:

A polynomial has a root of −2.

To find:

The factor that will divide evenly into the polynomial.

Solution:

We know that, if c is a root of a polynomial P(x), then (x-c) is a factor of polynomial P(x).

we have,

-2 is a root of polynomial.

⇒ (x-(-2)) is a factor of polynomial.

⇒ (x+2) is a factor of polynomial.

⇒ (x+2) will divide the polynomial completely.

Therefore, the factor (x+2) will divide evenly into the polynomial.