how do you factor by grouping

Question

mathstudent55 · Answer

Usually, factoring by grouping is used to factor a 4-term polynomial.
You factor a common factor out of the first two terms, and you factor a common factor out of the last two terms.
Then you factor out a common factor.

mathstudent55 · Answer

If you have a problem to do, post it, and we'll do it together.

anonymous · Answer

2c^4-8c^3+18c^2-72c

mathstudent55 · Answer

The first rule of factoring is to always try to factor a common factor first.
Can you factor a common factor out of all terms?

anonymous · Answer

I think -8c^3 & -72c

mathstudent55 · Answer

No. 
Factoring a common factor out of all terms is done by looking at all terms, both the coefficients (the numbers) and the variables, and seeing if they have a common factor.

Let's start with the coefficients.
What is the GCD of 2, -8, 18, and -72?
What is the largest number all those numbers are divisible by?

anonymous · Answer

2

mathstudent55 · Answer

Great.
Now let's look at the variables:
What is the GCF of $c^4, ~c^3, ~c^2, ~c$ ?

anonymous · Answer

1

mathstudent55 · Answer

How about c?
Every one of those is divisible by c, isn't it?

mathstudent55 · Answer

We're not looking at the number parts; we are now looking at the variable parts.

anonymous · Answer

yeah

mathstudent55 · Answer

That means the GCF for the entire polynomial is 2c.
Now we factor out 2c out of the whole thing.

mathstudent55 · Answer

$2c^4-8c^3+18c^2-72c$

$ = 2c(c^3 - 4c^2+9c - 36) $

You follow?

anonymous · Answer

yeah 
.

mathstudent55 · Answer

Ok, now we start with the factoring by grouping part.
Inside the parentheses, can you factor a common term out of $c^3$ and $-4c^2$?
Also, inside the parentheses, can you factor a common term out of $9c$ and $-72c$?

mathstudent55 · Answer

Remember, this factoring is similar to what we did before. Take out the largest number you can, and take out the largest variable part you can.

anonymous · Answer

okay I will be taking out c^3 and -72c?

mathstudent55 · Answer

No and no.
Let's do it piece by piece.
What do the terms $c^3$ and $-4c^2$ have in comon?

anonymous · Answer

the same varibles

mathstudent55 · Answer

c^3 is made up of 3 c's. c^2 is made up of 2 c's.
How many c's do they have in common?

mathstudent55 · Answer

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