For the polynomial below , -1 is a zero. G(x)=x^3+7x^2+24x+18. Express g(x) as a product of linear factors

Answer 1

x^3 + 7x^2 + 24x + 18

= (x+1)(x+3+2sqr2)(x+3-2sqr2)

divide x+1 into the cubic polynomial to get x^2 +6x +1

set it = 0 and solve for x

x = -3 + or - 2sqr2

x+3+2sqr2 = 0 and x+3-2sqr2 = 0

those are the other two linear factors: (x+3+2sqr2)(x+3-2sqr2)

third linear factor is (x+1)