Question

Help please: Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Answer 1

use the factor theorem to find what you want.
this theorem states that if a polynomial in x is divisible by (x - a) then f(a) = 0.

example:
is f(x) = x^3 - 2x^2 + 5x - 10 divisible by x - 2 ?
find f(2):
= 2^3 - 2(2)^2 +5(2) - 10 = 8 - 8 + 10 - 10 = 0
so x-2 is a factor of f(x)

Answer 2

Not a factor:

Answer 3

Is a factor.