So. Anyone know a simple way to explain factoring?

Question

Or not simple. It doesn't really matter, just someone help me!

I haven't taken an algebra course for a few years (I've been on a gemoetry course for about 2) and now I need to know how to factor for my homework.

Here are the questions:

1. 25x^2-16y^2
2. 3x^2+20x+25
3. 3x^3-39x^2+120x

Even if you can't explain them, if you culd list the steps to get the answer I'll be able to figure it out. Thank you so much!

Answer 1

1. 25x²-16y²
This is a difference of two squares and it factors by taking the square roots of the 1st & 2nd terms then multiplying their sum & difference like this:

(5x-4y)(5x+4y)

2. 3x²+20x+25
This one just factors by these rules:
1. look at the signs
if they are + + (like this case) or - + then you must ADD in step 3.
if they are - - or + - then you must SUBTRACT in step 3.
2. break up the number term into its factors (25 = 1x25 & 5*5) and the coeff of the x². (3 = 3x1 or 1x3)
3. Now look to see how you can manipulate the terms to ADD or SUBTRACT and get the middle term (20).
5x3 = 15 ADDED to 5x1 = 20
(3x+5)(x+5)
use FOIL to verify that these terms equal
3x²+20x+25

3. 3x³-39x²+120x
here 3x is common to all 3 terms, so bring it out to get:
3x(x² - 13x + 40)
Now the second expression, x² - 13x + 40, factors like we did for problem number 2, using the rules I gave above, and you will get:
3x (x-8) (x-5)
use FOIL on the ()() and you should get back x² - 13x + 40

Note that 8+5 is 13 (middle term)
and 8x5 is 40 (last term)

I think I covered all you need to know for this type of factoring.