SOLUTION: Have I correctly determined if the first polynomial is a factor of the second polynomial below and stated why it is? Problem 1: x + 1; x^3 + x^2 -4x - 4 YES it is - F(-1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Have I correctly determined if the first polynomial is a factor of the second polynomial below and stated why it is? Problem 1: x + 1; x^3 + x^2 -4x - 4 YES it is - F(-1)      Log On


   

Question 1190148: Have I correctly determined if the first polynomial is a factor of the second polynomial below and stated why it is?
Problem 1:
x + 1; x^3 + x^2 -4x - 4
YES it is - F(-1) because = 0

Problem 2:
x + 3; 2x^3 -11x^2 + 12x - 4
NO it is NOT Because F(-3) = -193
Thank you

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

You have used the remainder theorem correctly, and your computations are correct as well. Nice work.

Getting a remainder of zero on the first problem shows that x+1 is a factor of x^3 + x^2 -4x - 4

Getting a nonzero remainder on the second problem shows that x+3 is not a factor of 2x^3 -11x^2 + 12x - 4