Factor out greatest common factor of 3(x+5)^2 + 4(x+5)^4

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apburkey

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I have a problem where I need to factor out the GCF

Here is the problem 3(x+5)^2 + 4(x+5)^4 I know the GCF is (x+5)^2 but I do not know how to factor that out. If I could have an explanation or steps as to how you got to your answer that would be great.

It is a mutiple choice question and here are the choices they gave.

a) 7(x+5)^2
b) (x+5)^2(4x^2 + 103)
c) 7(x+5)
d) (x+5)^2(4x^2 +40x + 103)

From what I know from other problems I have done I think the answer would be either b or d .
 
apburkey said:
I need to factor out the GCF

3(x+5)^2 + 4(x+5)^4 I know the GCF is (x+5)^2 but I do not know how to factor that out.
Click to expand...
How would you factor the following?

. . . . .\(\displaystyle 3y^2\, +\, 4y^4\)

The process for your exercise works the exact same way! :wink:

Eliz.
 
3y^2 + 4y^4 I know the GCF is y^2 so not sure if this is right but this is how I factored it out. y^2(3+4y^2)
 
If I am doing this correctly after working out the problem like you recommended I tried my problem again and I got 7(x+5)^2 which is one of the choices.
 
No, that is not it. Expand out your choice and see if it ends up being the original. I do not think it is.

Think about it. How could \(\displaystyle 7(x+5)^{2}\) be correct. What happened to the other factor of (x+5)^2?.

What i mean is if you expand your choice you get \(\displaystyle 7x^{2}+70x+175\)

When you expand the original problem it is \(\displaystyle 4x^{4}+80x^{3}+603x^{2}+2020x+2575\)

How about factoring out \(\displaystyle (x+5)^{2}\). See?. That is the common thread. 4 and 3 do not share anything.

\(\displaystyle (x+5)^{2}[3+4(x+5)^{2}]\)

Now, expand what is in the parentheses and see if it is a choice.

This is the same techniques as if you had \(\displaystyle 3\cdot 13^{2}+4\cdot 13^{4}\)

What would we factor out?. The 13^2. \(\displaystyle 13^{2}(3+4\cdot 13^{2})\). See?. Same deal just with numbers instead of x's. But those x's represent numbers.
 
There ya' go. See, you can do it.

What you do is factor out something common amongst the terms. What does this one have in common?.

The only thing is (x+5)^2. Doesn't \(\displaystyle (x+5)^{2}\cdot (x+5)^{2}=(x+5)^{4}\).

You must know your exponent laws well to do these. Catching on now?.
 
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