Q:

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

Accepted Solution

A:
Answer:B. 1.-1,-2Step-by-step explanation:[tex]g(x) = x ^{3} + 2 {x}^{2} - x - 2[/tex]Substitute g(x)=0[tex]0 = {x}^{3} + 2 {x}^{2} - x - 2[/tex]Move the expression to the left[tex]0 - {x}^{3} - 2 {x}^{2} + x + 2 = 0[/tex]Factor out -x^2 from the expression[tex] - {x}^{2} \times (x + 2) + x + 2 = 0[/tex]Factor out (x+2) from the expression[tex](x + 2) \times ({x}^{2} + 1) = 0[/tex]When the product of the factor equals 0, at least one factor is 0[tex]x + 2 = 0[/tex][tex] - {x}^{2}+ 1 > = 0[/tex]Solve for x[tex]x = - 2 \\ x = - 1\\ x = 1[/tex]