Question

find the zeros of the function. (5. p(x) = x⁴ - 2x³ - 8x²

Explanation:

Step1: Factor out common term

$p(x) = x^2(x^2 - 2x - 8)$

Step2: Factor quadratic polynomial

$p(x) = x^2(x - 4)(x + 2)$

Step3: Set function to 0

$x^2(x - 4)(x + 2) = 0$

Step4: Solve for x

$x^2=0 \implies x=0$; $x-4=0 \implies x=4$; $x+2=0 \implies x=-2$

Answer:

$x = 0$ (multiplicity 2), $x = 4$, $x = -2$