Question

which expressions are factors of 6x^2 + 21x - 12
select three correct answers

Answer 1

To factor the quadratic expression \(6x^2 + 21x - 12\), we can start by looking for two numbers that multiply to \(6 \cdot (-12) = -72\) and add to \(21\) (the coefficient of \(x\)).

We find that the numbers \(24\) and \(-3\) fit these criteria, since:

- \(24 \times (-3) = -72\)
- \(24 + (-3) = 21\)

Next, we can rewrite the middle term \(21x\) using these numbers:

\[
6x^2 + 24x - 3x - 12
\]

Now, we can group the terms:

\[
(6x^2 + 24x) + (-3x - 12)
\]

Factoring out the common factors in each group gives us:

\[
6x(x + 4) - 3(x + 4)
\]

Now, we can factor out the common binomial factor \((x + 4)\):

\[
(6x - 3)(x + 4)
\]

We can also factor \(6x - 3\) further:

\[
3(2x - 1)(x + 4)
\]

Thus, the factors of \(6x^2 + 21x - 12\) are:

1. \(x + 4\)
2. \(2x - 1\)
3. \(3\)

Any combination of the three factors listed above can potentially work as a correct answer depending on the options given.

The correct factors of the expression are \(3\), \(x + 4\), and \(2x - 1\).