Question

select the correct answer. one of the factors of the polynomial ( x^3 + 5x^2 + 6x ) is ( (x^2 + 3x) ). what is the other factor?
a. ( x - 2 )
b. ( x + 2 )
c. ( x + 1 )
d. ( x - 1 )

Explanation:

Step1: Factor out common term

$x^3 + 5x^2 + 6x = x(x^2 + 5x + 6)$

Step2: Factor the quadratic

$x^2 + 5x + 6 = (x+2)(x+3)$

Step3: Compare with given factor

Given factor: $x^2 + 3x = x(x+3)$. Divide full factored polynomial by this:
$\frac{x(x+2)(x+3)}{x(x+3)} = x+2$

Answer:

B. $x+2$