Question

find all zeros for the polynomial function p(x) = x³ - 3x² - 5x + 15

Explanation:

Step1: Group polynomial terms

$P(x) = (x^3 - 3x^2) + (-5x + 15)$

Step2: Factor out common terms

$P(x) = x^2(x - 3) - 5(x - 3)$

Step3: Factor out $(x-3)$

$P(x) = (x - 3)(x^2 - 5)$

Step4: Set factors to 0, solve for $x$

$x - 3 = 0 \implies x=3$
$x^2 - 5 = 0 \implies x=\pm\sqrt{5}$

Answer:

B. $3, \sqrt{5}, -\sqrt{5}$