Polynomial Equation Help

Question

Solve each polynomial equation by factoring:

1. 5x³ + 10x² + 5x = 0
2. x³+ 2x² - 9x - 18 = 0

Answer 1

1) 5x (x^2 + 2x + 1) = 0

5x ( x + 1)(x+1) = 0

x=0, x=-1 , x=-1

2) x^2 (x+2) -9(x+2) = 0

(x+2)(x^2 - 9) = 0

(x+2)(x+3)(x-3) = 0

x=-2, x=-3 , x=3

Answer 2

1) Factor out 5x since all of the monomials [single terms] have a common factor of 5x

5x (x^2 + 2x + 1) = 0

Factor out the remaining polynomial- x^2 + 2x + 1

5x ( x + 1)(x+1) = 0

Set them all equal to zero and solve for x

x=0, x=-1 , x=-1

2) The first two monomials and the last two monomials both share the binomial x+2 in common, so factor that out

x^2 (x+2) -9(x+2) = 0

Then combine x^2 and -9 into one binomial and keep x+2 as the other binomial

(x+2)(x^2 - 9) = 0

Factor out x^2 and -9

(x+2)(x+3)(x-3) = 0

Set them all equal to 0 and solve for x

x=-2, x=-3 , x=3