Pre-cal factoring polynomials help! Please! Im begging you?

Question

I'm horrible at math and I have over 100 problems for pre-cal that are factoring polynomials and trinomials, so please can someone either refer me to a good website that explains it well for me, who absolutley sucks at math, or explain some in a way I can understand? Please?

Answer 1

What factoring is, is reversing the distributive property.  Some people think it's easy and obvious.  But a lot of people find it really tough.  Since you claim to "absolutely suck at math" I am going to tell you the long, but no guessing method to factoring trinomials, K?

Alright, 1st thing to ALWAYS try when factoring is looking for a GCF (greatest common factor).  That means something that can evenly be pulled out of every term.

ex.  5x^2 + 15x - 20  has a GCF of 5   (by the way x^2 means "x squared").  So you'd have 5(x^2 +3x -4)

ex.  24ab -12abc -7b^2c  has a GCF of b.

So you'd have 24a - 12ac -7bc

ex.  3x^2 + x - 2  has no GCF.

Got it so far?

Ok, for the rest of my explanation I will assume you have already looked for, and pulled out, any GCFs.

Lets review the distributive property:

Simplify (x+3)(2x-5)

(some people call the distributive property with 2 binomials FOIL)

2x^2 -5x +6x -15

which is 2x^2 +x -15.  Right?

Now the trick is, if you are given 2x^2 +x -15, how do you split it back up into (x+3)(2x-5) if you don't already know the answer?  Here goes:

step 1:  Multiply the first coefficient (number) by the last.

(2)(-15) = -30

.

step 2:  list all of the integer factor pairs of the value you got (ignore the sign right now):

1,30

2,15

3,10

5,6

step 3:  Now look at the sign of the number you're factoring.  If it is positive we will use 2 numbers of the same sign; if it's negative we'll use one positive, one negative.  Our value of -30 was negative -- so one of each sign,  WHAT WE ARE TRYING TO FIND IS THE PAIR OF INTEGER FACTORS THAT WHEN ADDED, GIVE YOU THE MIDDLE COEFFICIENT OF THE ORIGINAL EXPRESSION WE WERE TRYING TO FACTOR.

Our original expression was 2x^2 + x -15.  That means we are looking to get a -1 (that's what's in front of the x in the middle, see?).

If we are using one positive and one negative, the pair that will work is the 5 and 6 from our list.  +5 and -6.

step 4:  rewrite the original expression with the middle term split.

2x^2 +5x -6x -15

step 5:  Find the GCF for the FIRST HALF of the expression and the GCF for the SECOND HALF of the expression.

x(2x + 5) -3(2x+5)

Did you see how I did that?  I looked at the first two terms and pulled out the common x.  From the second two terms I could pull out a 3, but since it STARTED with a negative, that's why I pulled out a -3 (and that's why the sign changed on the 5).

step 6:  Now pull out the GCF for BOTH HALVES TOGETHER.

See how our first half has a (2x+5) and the second half does too?

Look way back up to the top of my answer when I talked about GCFs.  See how one 5 could be pulled out of 3 terms, and since it got put out in front of parentheses we only needed to write one 5?  Well, we're going to do the same thing with the (2x+5).

Pull it out front and you get:  (2x+5)(x-3).

Tah dah!  Factored.

Let's look at one more example to see if you have it:

ex. Factor 12x^2 + 11x +2

multiply 1st and last number: (12)(2) = 24

list factor pairs of that number:

1,24

2,12

3, 8

4,6

check the sign and choose the pair that gives you the middle value:

sign is positive -- we need to use two positive values to make an 11.

the pair that when ADDED gives me 11 is the 3 & 8.

Rewrite the original using the pair you found:

12x^2 + 3x + 8x + 2

Find the GCF for both HALVES.

3x(4x + 1) + 2(4x + 1)

Pull out the GCF that you created in the parentheses.

(4x +1)(3x +2)

And we're done!  If you want to check your work, just multiply that answer out and make sure it gives you what you wanted to factor.

WHEW!  Hope this helped.

Answer 2

i agree with the guy above me