Question

1. what is the factored form of $x^3 + 4x^2 - 5x$?

Explanation:

Step1: Factor out common term

$x^3 + 4x^2 - 5x = x(x^2 + 4x - 5)$

Step2: Factor quadratic polynomial

Find two numbers that multiply to $-5$ and add to $4$ (these are $5$ and $-1$).
$x^2 + 4x - 5 = (x + 5)(x - 1)$

Step3: Combine factors

Substitute the factored quadratic back into the expression.
$x(x^2 + 4x - 5) = x(x + 5)(x - 1)$

Answer:

$x(x + 5)(x - 1)$