Question

3x^2-9x+6?

Answer 1

This is just a trinomial.

Explanation:

It is neither an equality (`=`) nor an equality (`<, <=, >=,>`), 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 `3x^2-9x+6=0`, but that's just an assumption, the question does not state that.

Answer 2

`3(x - 2)(x - 1)`

Explanation:

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

`3x^2 -9x +6`

`3(x^2 -3x + 2)`

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

`3(x^2 color(red)(-3)x + color(red)2)`

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 xx 1 = 2`
`-2 xx -1 = 2`

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

`2 + 1 = 3`

`-2 + -1 = color(purple)(-3)`

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

`3(x^2 -3x + 2)`

`3(x^2 color(blue)(-2)x color(blue)(-1)x + 2)`

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

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

`3(x^2 -2x -1x + 2)`

`3[(x^2 -2x) + (-1x + 2)]`

`3[xcolor(green)((x -2)) + -1color(green)((x - 2))]`

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

`3(x -2)(x - 1)`

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!