Question

Use synthetic division to factorize this x^3 + 3x^2 -4. Show working out thanks.

Answer 1

Do you know the Rational Root Theorem? I think we will need it.

Answer 2

not quite, but can u just me the working out, as long as u show me the working out I should understand.

Answer 3

The rational root theorem generates a list of possible rational roots. From that list, we choose one root to test using synthetic division. No list means there are no divisiors to test.

If you are given a divisor, then synthetic division can be used to work out a quotient. But, here we have no way to get a divisor based on your current knowledge. So, I do not know how to approach the problem.

Answer 4

well I did figure out that one root is (x-1) and I did do the synthetic division, but I just got the wrong answer for some reason.

Answer 5

If (x-1) is a factor, then x = 1 is a root.

I'll run x = 1 through.

First, I have to get the coefficents.

x^3 + 3x^2 -4 = 1* x^2 + 3*x^2 + 0*x - 4

Answer 6

By factor theorem,
f(1) = 1^3 + 3(1)^2 -4 =0

x^3 + 3x^2 -4 = (x-1)(x^2+4x+4) = (x-1)(x+2)^2