Question

How does:

r^3+3r^2-4 = (r-1)(r^2+4r+4) ?

Answer 1

multiply it out... r^3 + 4r^2 + 4r - r^2 - 4r - 4 = r^3 + 3r^2 - 4. Got it?

Answer 2

Yes, but given the polynomial r^3 + 3r^2 - 4, how do you factor it to become (r-1)(r^2+4r+4)?

Answer 3

use long division. (r^3+3r^2-4)/(r-1)

Answer 4

Look for a root by trial and error. Possible roots are the factors of 4, which are 1, -1, 2, -2, and 4, -4. Always try first "1". Plug in 1 into r^3 + 3r^2 - 4 and you'll get 0. That means that "r - 1" is a factor. then divide r^3 + 3r^2 - 4 by "r - 1" and you'll get r^2+4r+4.

Answer 5

That makes sense, thank you!