express g(x) as a product of linear factors

Question

For the polynomial below, −1 is a zero.

g(x)=x^3

-3x^2+9x+13

express g(x) as a product of linear factors

Answer 1

divide the cubic by x+1 to get a quadratic

-1 1 -3 9 +13

__________

1 -4 13 0

= x^2 -4x +13

complete the square, use the quadratic formula to finds zeroes then change their signs and put an x in froonto them to get the factors the other linear factors are imaginary

x = 4/2 +/-.5sqr(16-52) = 2 + 3i and 2 -3i

factors are

(x+1)(x-2-3i)(x-2+3i)