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

The \(x^2\) terms are \(3x^2\) and \(2x^2\). Adding them: \(3x^2 + 2x^2 = 5x^2\)

Step2: Combine like terms for \(x\)

The \(x\) terms are \(-x\) and \(6x\). Adding them: \(-x + 6x = 5x\)

Step3: Write the simplified polynomial

The \(x^3\) term remains \(x^3\), the constant term remains \(-2\). So the simplified polynomial is \(x^3 + 5x^2 + 5x - 2\)

Answer:

\(x^3 + 5x^2 + 5x - 2\) (the first option)