Question

use factoring to solve the polynomial equation. check by substitution or by using a graphing utility and identifying x-intercepts.
$2x^4 - 8x^2 = 0$
find the solution set. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(use a comma to separate answers as needed. type each solution only once.)
b. there is no solution.

Explanation:

Step1: Factor out GCF

Factor $2x^2$ from the left side:
$2x^2(x^2 - 4) = 0$

Step2: Factor difference of squares

Rewrite $x^2-4$ as $(x-2)(x+2)$:
$2x^2(x-2)(x+2) = 0$

Step3: Set factors to zero

Set each factor equal to 0:
$2x^2=0$, $x-2=0$, $x+2=0$

Step4: Solve for x

Solve each equation:
From $2x^2=0$, $x=0$; from $x-2=0$, $x=2$; from $x+2=0$, $x=-2$

Step5: Verify solutions

Substitute $x=-2, 0, 2$ into original equation to confirm they satisfy it.

Answer:

A. The solution set is {-2, 0, 2}.