Question

Using only​ algebra, find a cubic function with the given zeros.
-2, 3, -7

the polynomial function is: f(x)=x^3+ (BLANK) x^2-13x-42

i can't figure out what BLANK is
Thank you!

Answer 1

(x+2)(x-3)(x+7) has those zeros
(x+2)(x^2 + 4x - 21)
= x*(x^2 + 4x - 21) +2*(x^2 + 4x - 21)
= x^3 + 4x^2 - 21 x + 2 x^2 + 8 x -42
= x^3 + 6 x^2 - 13 x - 42

Answer 2

if r is a root (zero) , then (x-r) is a factor

f(x) = (x + 2)(x - 3)(x + 7) ... multiply the binomials