Question

Factor. (How to solve?)

12x^3-23x^2+5x

Answer 1

Well what is common to all three variables?

Answer 2

x?

Answer 3

So first factor out the x and what do you have?

Answer 4

x(12x^2-23x+5)

Answer 5

Great now we can still factor (12x^2-23x+5) by using the quadratic formula..

Answer 6

I'm not sure where to go from here.

Answer 7

Do you know the quadratic formula?

Answer 8

No, we have not used it to solve these factoring problems.

Answer 9

Sorry, we have. Is it ax^2+bx+c?

Answer 10

Checking

Answer 11

Right. But then I am not sure what exactly I have to do.

Answer 12

No we need to factor 12x^2-23x+5..are you familiar with FOIL?

Answer 13

Somewhat. From what I know I have to find "ac" which would be 12x5, right?

Answer 14

http://ts1.mm.bing.net/th?&id=HN.608013394737893209&w=300&h=300&c=0&pid=1.9&rs=0&p=0

Answer 15

So what are the factors of 12? And what are the factors of 5?

Answer 16

1,2,3,4,6,12 and 1,5

Answer 17

Correct now we have to figure out what values to use. Since 5 has only 1 factor we can solve half our problem (ax-1)(bx-5). Do you see this? Do you understand why it is minus for both equations?

Answer 18

Because both negatives equal positive?

Answer 19

Correct and also because in the equation ax^2+bx+c C is positive but bx is negative. Now the fun part. WE need to get (ax-1)(bx-5) to equal 12x^2-23x+5, we do this through trial and error of plugging in our factors for 12 for the values of a and b. Do you understand?

Answer 20

I don't really understand :(

Answer 21

Ok look at the factors for 12..Let's take 2 and 6 and plug them into our factor we get
(2x-1)(6x-5) now does that equal 12^2-23x+5?

Answer 22

No, it equals 12x^2-26x+5.. Or is that not correct?

Answer 23

Good..now try another factor say.3 and 4. Solve and see if it equals 12^2-23x+5?

Answer 24

12x^2-20x+5?

Answer 25

Might want to check that one

Answer 26

(3x-1)(4x-5), right?

Answer 27

Yes

Answer 28

Check the 20x

Answer 29

19x instead?

Answer 30

Now flip the 3 and the 4 around and solve,

Answer 31

(4x-1)(3x-5)

Answer 32

12x^2-23x+5?

Answer 33

So that is our other factors. So what is the answer?

Answer 34

x(4x-1)(3x-5)?

Answer 35

Great job...trust me this gets easier the more you practice...

Answer 36

Oh my gosh, it is right. I submitted it and got the correct answer... you made it so much more easier to understand than the textbook and online instruction. Thank you so much, I spent hours on this problem.