Solve the polynomial equation by factoring.
-$$2 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 0$$
A) $- 1,1 , - 2$
B) $1 , - 2$
C) $1 , - 1,2$
D) $- 1 , - 2$

Question

Quizplus · Accepted Answer

The given polynomial can be factored by grouping. First, group the terms: $(2x^3 + 4x^2) - (2x + 4)$. Factoring out the common terms gives $2x^2(x + 2) - 2(x + 2)$. Factoring by grouping, we get $(x + 2)(2x^2 - 2) = (x + 2)(2)(x^2 - 1)$. Further factoring gives $(x + 2)(2)(x + 1)(x - 1)$. Setting each factor equal to zero gives the roots $x = -2, x = -1, x = 1$.

Solve the Polynomial Equation by Factoring 2x3+4x2−2x−4=02 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 02x3+4x2−2x−4=0

Solve the Polynomial Equation by Factoring $2 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 0$