Question

multiplying polynomials and simplifying expressions
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?
$x^3 + 2x^2 + 8x - 2$
$x^3 + 11x^2 - 2$
$x^3 + 5x^2 + 5x - 2$
$x^3 + 10x^2 - 2$

Explanation:

Step1: Combine like \(x^2\) terms

The \(x^2\) terms are \(3x^2\) and \(2x^2\). So, \(3x^2 + 2x^2 = 5x^2\).

Step2: Combine like \(x\) terms

The \(x\) terms are \(-x\) and \(6x\). So, \(-x + 6x = 5x\).

Step3: Write the simplified expression

The original expression is \(x^3 + 3x^2 - x + 2x^2 + 6x - 2\). After combining like terms, we have \(x^3 + 5x^2 + 5x - 2\).

Answer:

\(x^3 + 5x^2 + 5x - 2\) (the third option among the given choices)