Question

CAN SOMEONE TEACH ME HOW TO FACTOR

Answer 1

List a few examples that you are trying to factor.

Answer 2

5x^2-3x+3

Answer 3

First Lesson: Become wonderful at Factorization of Integers.

ax^2 + bx + c = 0

Find ALL the factorizations of 'a'.
Find ALL the factorizations of 'c'.

3x^2 + bx + 2 = 0

Simple:
All the factorizations of 3 are 1*3 and 3*1
All the factorizations of 2 are 1*2 and 2*1

12x^2 + bx + 15 = 0

Not so Simple:
All the factorizations of 12 are 1*12, 2*6, 3*4, 4*3, 6*2, 12*1
All the factorizations of 15 are 1*15, 3*5, 5*3, and 15*1

Okay, there is Lesson #1. Try some.

7x^2 + bx + 9 = 0

8x^2 + bx + 24 = 0

Challenge Problem:

(3/2)x^2 + bx + 5 = 0

Answer 4

can you show me more steps

Answer 5

You haven't done your homework assignment.

Answer 6

idu how

Answer 7

It's up there at the bottom of my first post. Demonstrate those factorings.

Answer 8

oh ok

Answer 9

In addition there are several websites and YouTube videos that show step-by-step procedure to factor quadratic expressions. Here is one such website:
http://www.purplemath.com/modules/factquad.htm

Answer 10

Yup. I like PurpleMath. There are plenty of resources.

Answer 11

7x^2 + bx + 9 = 0
All the factorizations of 7 are 1*7
All the factorizations of 9 are 1*9 , 3*3,
8x^2 + bx + 24 = 0
All the factorizations of 8 are 2*4 and 8*1
All the factorizations of 24 are 1*24 , 2*12, 6*4 and 3*8
Challenge Problem:
(3/2)x^2 + bx + 5 = 0
All the factorizations of 3/2 are 3/2*1
All the factorizations of 5 are 1*5

Answer 12

@tk

Answer 13

@tkhunny

Answer 14

Okay, a couple of things.

For 'a', all you really need is the one direction, 1*7 will serve about as well as 7*1.
For 'c', this is not the case. You need BOTH. 1*7 and 7*1. Don't get caught up in thinking there is only one pair when order matters.

As for the challenge problem, (3/2)x^2 + bx + 5 = 0
You should have noted that factorization isn't particularly useful unless you have INTEGERS. You should first have multiplied the entire equation by 2.

3x^2 + 2bx + 10 = 0

Now we see, a) 1*3 or 3*1
c) 1*10, 2*5, 5*2, 10*1

Are we making any sense?

Answer 15

yes

Answer 16

Okay, now we get to think about the sign of c. If it is positive, we are done with possibilities. If it is negative, we just doubled our potential work.

3x^2 + bx + 2 = 0

Simple:
All the factorizations of 2 are 1*2 and 2*1

3x^2 + bx - 2 = 0

Simple:
All the factorizations of 2 are 1*2 and 2*1, but to get -2, that is now
These (-1)*2 and (-2)*1 and 1*(-2) and 2*(-1)

Okay, now we have ALL the possibilities written down. There are LOTS of Rational Numbers. It shoudl not be surprising that there can be quite a list.

Still making sense?

12x^2 + bx + 15 = 0 Not so Simple: All the factorizations of 12 are 1*12, 2*6, 3*4, 4*3, 6*2, 12*1 All the factorizations of 15 are 1*15, 3*5, 5*3, and 15*1