Question

Factor the trinomial below.
6x^2-9x-6
03(2x + 1)(x- 6)
03(2x+ 2)(x-1)
03(2x + 1)(x-2)
03(2x + 6)(x- 1)

Answer 1

To factor the trinomial \(6x^2 - 9x - 6\), we can first look for a common factor in all the terms.

The common factor of \(6x^2\), \(-9x\), and \(-6\) is \(3\). So, we can factor out \(3\):

\[
6x^2 - 9x - 6 = 3(2x^2 - 3x - 2)
\]

Now, we need to factor the quadratic inside the parentheses: \(2x^2 - 3x - 2\).

To factor \(2x^2 - 3x - 2\), we look for two numbers that multiply to \(2 \cdot (-2) = -4\) and add to \(-3\).

The numbers that satisfy this are \(-4\) and \(1\).

Next, we rewrite \(-3x\) using these numbers:

\[
2x^2 - 4x + x - 2
\]

Now, we group the terms:

\[
(2x^2 - 4x) + (x - 2)
\]

Factoring out the common factors from each group, we get:

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

Now we can factor out the common binomial \((x - 2)\):

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

Putting it all together with the common factor we factored out earlier:

\[
6x^2 - 9x - 6 = 3(2x + 1)(x - 2)
\]

Thus, the trinomial \(6x^2 - 9x - 6\) factors to:

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

So, the correct answer from the options given is:

\(\boxed{03(2x + 1)(x - 2)}\)