Question

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

binomial will be divisor if is a root of polinomial

Answer 2

first one
Create a sample problem that has a binomial which IS a factor of the polynomial being divided,

start with your polynomial in factored for, make up anything where one is a "binomial" say
\[(x^2+2x+1)(x-4)\] multiply out, and then you will be sure that \(x-4\) is a factor of your result

Answer 3

for the second one, you can take your answer for the first one and add some number to it. then you can be sure that \(x-4\) is not a factor

Answer 4

Thank You Alot :)

Answer 5

yw