1. ## (Algebra I) Confused about factoring polynomials

Hello all,

So far I have a fairly good understanding of factoring two and three term polynomials (I thought I did). I can find the GCF and understand how it applies. I've been solving the following types of problems through my homework:
-9a5 + 18a2 - 3a = -3a(3a4 - 6a + 1) and 5x4 - 20x = 5x (x3 - 4).

But textbook suddenly showed:
Factor: 5(x + 3) + y(x + 3)

Solution:
The binomial (x + 3) is the greatest common factor. Use the distributive property to factor out (x + 3).

5(x + 3) + y(x + 3) = (x + 3) (5 + y)

My problem:
I don't understand how (x + 3) is a factor because so far, I've only see factors to be whole numbers and variables. How do you find a GCF from (x + 3)?? Is this an example of factoring by grouping? That's in the next section so I haven't covered that yet.

I really want to understand this section before I get back into class so that my professor's examples make more sense.

Thank you.

2. ## Re: (Algebra I) Confused about factoring polynomials

Suppose $\displaystyle u=x+3$. Then, you have $\displaystyle 5u+yu = u(5+y)$. Replace $\displaystyle u$ by $\displaystyle (x+3)$. If you want to see it with whole numbers, plug in x=0. Try again for x=1. Keep trying for various values of x until you spot a pattern. A large part of learning Mathematics is training your brain to spot patterns quickly.

My point with the replacement of $\displaystyle x+3$ with $\displaystyle u$ was that you can start to think of $\displaystyle (x+3)$ as a variable, as well. In this case, $\displaystyle u$ is a dependent variable (it depends on the value of $\displaystyle x$) while $\displaystyle x$ is an independent variable (we have no variables listed upon which the value of $\displaystyle x$ depends).

3. ## Re: (Algebra I) Confused about factoring polynomials

Doesn't you book have a definition of the word "factor"? If it does, you should realize that there is no requirement that a factor be a single term.

4. ## Re: (Algebra I) Confused about factoring polynomials

Originally Posted by HallsofIvy
Doesn't you book have a definition of the word "factor"? If it does, you should realize that there is no requirement that a factor be a single term.
No it doesn't but I understand what you mean. Thanks

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