Question

Find the expression that is equivalent to 3x2+2x−5x−2x2+2
.(1 point)
Responses

(x+2)(x−2)
left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis

(x+1)(x+2)
left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis

(x−2)(x−1)
left parenthesis x minus 2 right parenthesis left parenthesis x minus 1 right parenthesis

(3x+2)(x+1)

Answer 1

To simplify the expression \(3x^2 + 2x - 5x - 2x^2 + 2\), we first combine like terms:

1. Combine the \(x^2\) terms:
\[
3x^2 - 2x^2 = x^2
\]

2. Combine the \(x\) terms:
\[
2x - 5x = -3x
\]

So the expression simplifies to:
\[
x^2 - 3x + 2
\]

Next, we will factor this quadratic expression. We need to find two numbers that multiply to \(2\) (the constant term) and add to \(-3\) (the coefficient of \(x\)). The numbers \(-1\) and \(-2\) fit this requirement, as:
\[
-1 \times -2 = 2 \quad \text{and} \quad -1 + -2 = -3
\]

Thus, we can factor the expression as:
\[
(x - 1)(x - 2)
\]

Now let's compare this to the provided options. Since there is no \((x - 1)(x - 2)\) option present, we'll take a closer look at the given choices.

None of the choices seem to match what we obtained from factoring \(x^2 - 3x + 2\), which would imply that other options are incorrect based on your question.

The correct factoring should lead to:
\[
\text{Factored form of } x^2 - 3x + 2 \text{ is } (x-1)(x-2).
\]

Please check the options provided again to verify their accuracy. If we were to determine it based on the common factors, it doesn't match any of the selections you presented.