Part 1: 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.

Question

I do not get this at all and help would mean so much

Answer 1

the divisor is a factor if the remainder is zero

Just as you know that 5 is a factor of 35 because 35/5 has zero remainder.

For example,

(2x-1)(x+2)(3x+7) / (x+2)
= (6x^3+23x^2+15x-14)/(x+2)

we know that the remainder is zero, because we constructed it that way. To make that a fraction where the divisor is NOT a factor, just change any of the coefficients. Then the divisor will no longer go in evenly.