Question

Find the expression that is equivalent to 3x2+2x−5x−2x2+2

(3x+2)(x+1)

(x+1)(x+2)

(x−2)(x−1)

(x+2)(x−2)

Answer 1

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

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

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

3. The constant term is already \( +2 \).

Now, we can rewrite the expression:
\[
x^2 - 3x + 2
\]

Next, we can factor \( x^2 - 3x + 2 \). We need to find two numbers that multiply to \( +2 \) (the constant term) and add to \( -3 \) (the coefficient of \( x \)).

The pair of numbers that meet these criteria is \( -1 \) and \( -2 \).

Thus, we can factor the quadratic as follows:
\[
x^2 - 3x + 2 = (x - 1)(x - 2)
\]

Finally, looking at the answer choices given, the correct factored form that corresponds to this expression is:
\[
(x - 2)(x - 1)
\]

Thus, the equivalent expression is:
\[
\boxed{(x - 2)(x - 1)}
\]