Question

3x^2-x-2

Answer 1

To factor the quadratic expression \(3x^2 - x - 2\), we are looking for two numbers that multiply to \(3 \times -2 = -6\) and add to \(-1\) (the coefficient of \(x\)).

The two numbers that satisfy these conditions are \(2\) and \(-3\).

We can rewrite the middle term \(-x\) using these two numbers:

\[
3x^2 + 2x - 3x - 2
\]

Next, we can group the terms:

\[
(3x^2 + 2x) + (-3x - 2)
\]

Factoring out the common factors in each group gives:

\[
x(3x + 2) - 1(3x + 2)
\]

Now, we can factor out the common binomial \(3x + 2\):

\[
(3x + 2)(x - 1)
\]

So, the factorization of the quadratic expression \(3x^2 - x - 2\) is:

\[
(3x + 2)(x - 1)
\]