Question

find the expression that is equivalent to 3x^2+2x-5x-2x^2+2
(x+2)(x-2)
(3x+2)(x+1)
(x+1)(x+2)
(x-2)(x-1)

Answer 1

To simplify the expression \( 3x^2 + 2x - 5x - 2x^2 + 2 \), we can 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. The constant term is \( +2 \).

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

Next, we need to factor \( x^2 - 3x + 2 \). We are looking for two numbers that multiply to \( 2 \) (the constant term) and add to \( -3 \) (the coefficient of the \( x \) term). These numbers are \( -1 \) and \( -2 \).

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

Now, we can compare this to the given options:
1. \( (x + 2)(x - 2) \)
2. \( (3x + 2)(x + 1) \)
3. \( (x + 1)(x + 2) \)
4. \( (x - 2)(x - 1) \)

The correct equivalent expression for \( 3x^2 + 2x - 5x - 2x^2 + 2 \) is:
\[
(x - 2)(x - 1)
\]

Therefore, the answer is:
\[
(x - 2)(x - 1)
\]