Question

Find the polynomial function with leading coefficient 3 that has the given degree and zeros.

a.) Degree 3, with -2, 1, and 4 as zeros

Answer 1

Answer: x^3 - 3x^2 - 6x + 8

Answer 2

So you know that there are three zeroes, and that it is to the 3rd degree, so you know that there are going to be 3 terms initially.

(x+2)(x-1)(x-4) - You can multiply by 3 at the end

x^2 - x + 2x -2
(x^2 + x - 2)(x - 4)

x^3 - 4x^2 + x^2 - 4x - 2x + 8
x^3 - 3x^2 - 6x + 8

f(x) = 3x^3 - 9x^2 - 18x + 24