Question

the product of a binomial and a trinomial is $x^{3}+3x^{2}-x + 2x^{2}+6x - 2$. which expression is equivalent to this product after it has been fully simplified?
$\bigcirc\\ x^{3}+5x^{2}+5x - 2$
$\bigcirc\\ x^{3}+2x^{2}+8x - 2$
$\bigcirc\\ x^{3}+11x^{2}-2$
$\bigcirc\\ x^{3}+10x^{2}-2$

Explanation:

Step1: Identify like terms

Group terms by exponent:
$x^3$, $3x^2+2x^2$, $-x+6x$, $-2$

Step2: Combine $x^2$ terms

$3x^2 + 2x^2 = 5x^2$

Step3: Combine $x$ terms

$-x + 6x = 5x$

Step4: Assemble simplified expression

Combine all simplified terms.

Answer:

$x^3 + 5x^2 + 5x - 2$ (Option A)