factor completly?

Question

factor completly 6x^2 - 17x + 12 what process do I use and how do I go about factoring this problem?

Answer 1

Split the -17x into two terms, then factor by grouping. Here's how:

Mulitply 6 (from the 6x² term) by 12 (from the constant term on the end) to get a product of 72. Your job is to now find two factors of (numbers that multiply to) +72 that have a sum of (add to) -17 (from the -17x term). With a positive product and a negative sum, both of the numbers you come up with must be negative. List 'em 'til you get 'em. Sooner or later, I'm sure you'll find -9 and -8.

So, split the -17x into two terms.
6x² - 17x + 12
6x² - 9x + -8x + 12
Now factor by grouping.
(6x² - 9x) + (-8x + 12). [Factor GCF from each group.]
3x(2x - 3) + -4(2x - 3). [Combine like groups.]
(3x - 4)(2x - 3).

Answer 2

First, factor out the six to 3 and 2

(3x ) (2x )

Factor out the 12. Well here it is logical to say that 12 is equal to 4 x 3 or -4 x -3. Let's use - 4 and -3 since we have a mid term of a NEGATIVE -17

(3x - 4)(2x - 3) is the answer.
Because (3x)(-3) = -9x -4(2x) = -8x -9x - 8x = -17x

Answer 3

6x^2 - 17x + 12

Two numbers that multiply to get (6 * 12) and add to get (-17) are -9 and -8.

6x^2 - 9x - 8x + 12

Group this so you can factor it.

(6x^2 - 9x) + (-8x +12)

The GCF of 6x^2 and -9x is 3x; the GCF of -8x and 12 is -4.

3x(2x - 3) - 4(2x - 3)

Factor out (2x-3).

(2x - 3)(3x - 4)

Answer 4

(3x-4)(2x-3)...it's the reverse of foil...it's mainly trial and error...3x & 2x are factors of 6x^2...then both signs are negative because the 12 is positive (negative * negative = positive)...4 * 3 = 12...so you have the answer...the order of them does matter...for example, you can't have (3x-3)(2x-4)

Answer 5

x = 3/2 and x = 4/3. I cannot explain this with the limited font available on Yahoo. You can email me if you wish.

Answer 6

Go to the bottom of this page for an example

http://www.purplemath.com/modules/factquad2.htm

Answer 7

(2x - 3)(3x - 4)

I use x = (-b ± sqrt(b^2 - 4ac))/(2a)

if i don't know how to factor it.