# 3x^2-9x+6?

Apr 16, 2018

This is just a trinomial.

#### Explanation:

It is neither an equality ($=$) nor an equality ($< , \le , \ge , >$), therefore the question isn't clear. What exactly is it that you would like an explanation/help ?

If there is nothing else but just this, it's just a trinomial that has no real point.

MAYBE you mean $3 {x}^{2} - 9 x + 6 = 0$, but that's just an assumption, the question does not state that.

Apr 16, 2018

$3 \left(x - 2\right) \left(x - 1\right)$

#### Explanation:

Since the numbers all have a common factor of $3$, we can factor that out to simplify the question a little:

$3 {x}^{2} - 9 x + 6$

$3 \left({x}^{2} - 3 x + 2\right)$

Now the trick of factoring out this trinomial is to pay attention to these two numbers:

$3 \left({x}^{2} \textcolor{red}{- 3} x + \textcolor{red}{2}\right)$

We need to find two numbers that multiply together to make $+ 2$, and add together to make $- 3$. Let's start out by figuring out all the pairs that multiply together to make positive $2$:

$2 \times 1 = 2$
$- 2 \times - 1 = 2$

Which of these pairs adds together to make $- 3$?

$2 + 1 = 3$

$- 2 + - 1 = \textcolor{p u r p \le}{- 3}$

The second one does, so we can change the inside a little:

$3 \left({x}^{2} - 3 x + 2\right)$

$3 \left({x}^{2} \textcolor{b l u e}{- 2} x \textcolor{b l u e}{- 1} x + 2\right)$

Because $- 2 x + - 1 x = - 3 x$, we can change the middle term.

Now we will group these into two groups and factor out the common terms:

$3 \left({x}^{2} - 2 x - 1 x + 2\right)$

$3 \left[\left({x}^{2} - 2 x\right) + \left(- 1 x + 2\right)\right]$

$3 \left[x \textcolor{g r e e n}{\left(x - 2\right)} + - 1 \textcolor{g r e e n}{\left(x - 2\right)}\right]$

Now we can actually factor out $\left(x - 2\right)$ since each group has one of those and this is what we are left:

$3 \left(x - 2\right) \left(x - 1\right)$

Here is a really helpful Khan Academy video on this exact thing, where he can talk you through each individual step since this is a really confusing and complicated process!