Question

solve for x.
$x^3 + 5x^2 - 9x - 45 = 0$
$x = ?, , $
enter the solutions in ascending order.

Explanation:

Step1: Group terms for factoring

$x^3 + 5x^2 - 9x - 45 = (x^3 + 5x^2) + (-9x - 45)$

Step2: Factor out common terms

$x^2(x + 5) - 9(x + 5) = 0$

Step3: Factor binomial

$(x^2 - 9)(x + 5) = 0$

Step4: Factor difference of squares

$(x - 3)(x + 3)(x + 5) = 0$

Step5: Solve for x

Set each factor to 0:
$x - 3 = 0 \implies x=3$
$x + 3 = 0 \implies x=-3$
$x + 5 = 0 \implies x=-5$

Step6: Order solutions ascendingly

Sort $-5, -3, 3$

Answer:

$x = -5, -3, 3$