3x^2-9x+6?

2 Answers
Apr 16, 2018

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.

Apr 16, 2018

#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!