If you divide a polynomial by a binomial, how do you know if the binomial is a factor of the polynomial?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminate) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The polynomial with two terms is called a binomial.

For example `x^3+2x+2` is a polynomial and `x+2` is a binomial.


We can use the remainder theorem to find out whether a binomial is a factor of a polynomial.

In remainder therem it states that  a polynomial f(x) is divided by (x-a) which is a binomial the remainder is given by f(a).

So when it comes to a factor f(a) = 0


Now the problem is clear.

You can substitute the value of binomial (which binomial equate to 0) to the polynomial and check whether the remainder is 0.If so it is a factor otherwise not.


Just see the example for more.....

polynomial `f(x) = x^2+2x+1`

Binomial `= (x+1)`


`(x+1) = 0` when `x = -1`

`f(-1) = (-1)^2+2(-1)+1 = 0`


So `(x+1)` is a factor of `x^2+2x+1.`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial