For the polynomial below, 1 is zero. Express f(x) as a product of linear factors

Question

For the polynomial below, 1 is zero. Express f(x) as a product of linear factors

f(x)=x^3+5x^2+7x-13

Answer 1

divide x-1 into x^3 +5x^2 +7x -13 to get x^2+6x +13

use long or synthetic division

(x-1)(x^2+6x+13) = x^3+5x^2+7x-13

but you want linear factors

x^2+6x+13 doesn't factor easily

x^2 +6x + 9 + 13-9= 0 by completing the square

= (x+3)^2 = -4

x+3 = sqr(-4)

x =-3+ or - 2i

factors are (x+3-2i) and (x+3+2i)

(x-1)(x+3-2i)(x+3+2i) = x^3 +5x^2 + 7x -13