Question

solve the following polynomial equations by grouping and factoring,
$x^3 - 4x^2 - 4x + 16 = 0$.

select one:
a. $x = 4, 2$
b. $x = 0, -4, 2$
c. $x = 4, 2, -2$
d. $x = 2, 4, -4$

Explanation:

Step1: Group the polynomial terms

$x^3 - 4x^2 - 4x + 16 = (x^3 - 4x^2) + (-4x + 16)$

Step2: Factor out common terms

$x^2(x - 4) - 4(x - 4)$

Step3: Factor out shared binomial

$(x^2 - 4)(x - 4)$

Step4: Factor difference of squares

$(x - 2)(x + 2)(x - 4)$

Step5: Solve for x

Set each factor equal to 0:
$x - 2 = 0 \implies x=2$
$x + 2 = 0 \implies x=-2$
$x - 4 = 0 \implies x=4$

Answer:

C. $x = 4, 2, -2$