Question

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

(x+2)(x−2)
open paren x plus 2 close paren times open paren x minus 2 close paren - no response given

(x−2)(x−1)

Answer 1

Let's simplify the expression \(3x^2 + 2x - 5x - 2x^2 + 2\).

1. Combine the like terms:
- For \(x^2\) terms: \(3x^2 - 2x^2 = 1x^2\) (or just \(x^2\))
- For \(x\) terms: \(2x - 5x = -3x\)

So, we have:
\[
x^2 - 3x + 2
\]

2. Now we can factor the quadratic expression \(x^2 - 3x + 2\):
- We are looking for two numbers that multiply to \(2\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)).
- The numbers \(-1\) and \(-2\) fit this requirement, as:
\(-1 \times -2 = 2\) and \(-1 + -2 = -3\).

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

Therefore, none of the first two provided options, which were \((x + 2)(x - 2)\) or \((x - 2)(x - 1)\), contain the correct expression. The correct factored form is:
\[
(x - 1)(x - 2)
\]

Hence, the correct response is:
\((x - 2)(x - 1)\) (which is indeed the second option).