Question

Select the expression that is equivalent to 2x3+11x2−21xx2+3x for x ≠ −3 or 0 .

Answer 1

Answer:

$\frac{(2x-3)(x+7)}{x+3}$

Step-by-step explanation:

Given

$\frac{2x^3+11x^2-21x}{x^2+3x}$

Required

Select equivalent expression

$\frac{2x^3+11x^2-21x}{x^2+3x}$

Factorize the numerator and denominator

$\frac{x(2x^2+11x-21)}{x(x+3)}$

Divide by x/x

$\frac{2x^2+11x-21}{x+3}$

Expand the numerator

$\frac{2x^2+14x-3x-21}{x+3}$

Factorize the numerator

$\frac{2x(x+7)-3(x+7)}{x+3}$

$\frac{(2x-3)(x+7)}{x+3}$

Hence, the equivalent expression is:

$\frac{(2x-3)(x+7)}{x+3}$