Question

1. $2x^4 = 24x^2$

Explanation:

Step1: Rearrange equation to zero

$2x^4 - 24x^2 = 0$

Step2: Factor out common term

$2x^2(x^2 - 12) = 0$

Step3: Set each factor to zero

$2x^2 = 0$ and $x^2 - 12 = 0$

Step4: Solve for $x$ from first factor

$x^2 = 0 \implies x = 0$

Step5: Solve for $x$ from second factor

$x^2 = 12 \implies x = \pm\sqrt{12} = \pm2\sqrt{3}$

Answer:

$x = 0$, $x = 2\sqrt{3}$, $x = -2\sqrt{3}$