Question

Explain how a four-term polynomial is factored by grouping and when a quadratic trinomial can be factored using this method. Include examples in your explanation

Answer 1

@wio @eliassaab

Answer 2

someone please help :(

Answer 3

@Preetha

Answer 4

1. Break up the polynomial into sets of two
2. Find the GCF of each set and factor it out
3. Factor again as many times as you can

Answer 5

could you break it down a little more? I'm really confused on this question

Answer 6

\[x^3+x^2+x-1 \]
This will be an example.

Yes of course, I'm going to show you :)

Answer 7

So x^3 and x^2 can be in one group, and x and -1 can be in another.

That is step one, breaking it up into two's

Does that part make sense?

Answer 8

Yes

Answer 9

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

Answer 10

So the second part you have to do is find the greatest common factor of each set. So for the first one, x^2 is the greatest common factor, and for the second one, -1 will be the greatest common factor

Answer 11

I thought you said x and -1 could be in one group? Why is the -1 in the middle

Answer 12

All I did was factor it out :) It can also look like (x^3+x^2) - (x+1) and it'll be the same thing. Make sense?

Answer 13

yes

Answer 14

So, step 2 was find the GCF. You've learned about that right?

Answer 15

Yes

Answer 16

So after you take out the x^2 and -1, your equation is going to look like this:
\[x^2(x+1) -1(x+1)\]
Agreed?

Answer 17

yes :)

Answer 18

So this next part is kinda tricky, just go with me on it.

(x+1) is going to be it's own term, since it's there in both places.
The x^2 and -1 is going to make it's own term.

\[(x^2-1)(x+1)\]
It's going to look just like that

Answer 19

Ok i understand so far

Answer 20

Okay, and x^2-1 can be factored further. You've done FOIL right?

Answer 21

I haven't heard of it

Answer 22

Okay. You might recognize it, or if you haven't learned it yet, don't worry, you will.