Question

Find the expression that is equivalent to 3x^2 + 2x - 5x - 2x^2 + 2.
(x + 1) (x + 2)
(x - 2) (x - 1)
(x + 2) (x - 2)
(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:
\[
2x - 5x = -3x
\]

3. Now, we can write the expression with the simplified terms:
\[
x^2 - 3x + 2
\]

Next, we will factor the quadratic expression \( x^2 - 3x + 2 \).

To factor it, we look for two numbers that multiply to \( 2 \) (the constant term) and add up to \( -3 \) (the coefficient of \( x \)). The numbers \( -1 \) and \( -2 \) meet these criteria.

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

Now let's compare this with the provided options:
- \( (x + 1)(x + 2) \)
- \( (x - 2)(x - 1) \)
- \( (x + 2)(x - 2) \)
- \( (3x + 2)(x + 1) \)

The correct answer is \( (x - 2)(x - 1) \).