Select the correct answer What are the real zeros of the function g(x) = x^3 + 2x^2 - x - 2? A. 1,-1,2 B. 1,-1, -2 c. 1,-1 D. 2, -2, 1

Question

asked Jul 12, 2020 180k views

2 Answers

Masa Sakano · Answer 1 · 2020-07-17T16:46:09+0000

Answer:

B. 1.-1,-2

Explanation:

$g(x) = x ^(3) + 2 {x}^(2) - x - 2$

Substitute g(x)=0

$0 = {x}^(3) + 2 {x}^(2) - x - 2$

Move the expression to the left

$0 - {x}^(3) - 2 {x}^(2) + x + 2 = 0$

Factor out -x^2 from the expression

$- {x}^(2) * (x + 2) + x + 2 = 0$

Factor out (x+2) from the expression

$(x + 2) * ({x}^(2) + 1) = 0$

When the product of the factor equals 0, at least one factor is 0

x + 2 = 0

$- {x}^(2)+ 1 > = 0$

Solve for x

$x = - 2 \\ x = - 1\\ x = 1$