factoring i need to understand..?

Question

x2 - 8x + 12

Factor this quadratic and show all work so i can understand please.

Answer 1

x² - 8x + 12
Step 1 is to find factors for x²
(x*******)(x*****)

Step 2 is to find factors for 12 that combine with x and x to give 8x
(x******6)(x******2)

Step 3 is to insert appropriate signs
(x - 6) (x - 2)

Check
x (x - 2) - 6 (x - 2)
= x² - 2x - 6x + 12
= x² - 8x + 12 (as required)

Answer 2

to factor quadratics where the coefficient of x2 is 1 (there is no number in front of x2)
consider the constant (last term), which in this case is 12
list all factors of 12
you want to find a pair of factors that add up to the cofficient of x, which in this case is (-8)
our choices are (1, 12), (2, 6), (3, 4), (-1, -12), (-2, -6), (-3, -4)
if u add each group of numbers only (-2) and (-6) will add up to (-8)
so we can rewrie x2 -8x +12 as x2 -2x -6x + 12
now that are expression has 4 terms we can factorize by grouping
factoring x2 - 2x we get x(x - 2) and
factoring -6x +12 we get -6(x - 2)
as (x - 2) belongs to both terms this is our first factor
and (x - 6) is our second factor
x2 - 8x + 12 = (x - 2)(x - 6)

Answer 3

x2 - 8x +12
(x-6)(x-2)

Ok easy..
we know you need a x2 so in each parenthesis you need an x.
then really quick..
You need -8x which is just which two numbers when added will = -8?? then which of these numbers = +12??

Ex:
x+y = -8
xy = 12
we know -1-7, -2-6, -3-5 and -4-4 = -8
for these #s we know as they are multiplied we get +7, +12, +15 and +16
so your answer is (x-2)(x-6)

just remember x's in the front = x2 when multiplied, then when the two numbers are added they equal the middle x. then those numbers must be multiplied to = the 3rd number
not really confusing once you get the tips and tricks

Answer 4

Use AC method.

find two numbers that multiply to AC and add to B.

A = 1
B = -8
C = 12

AC = 1*12 = 12
B = -8

so find two numbers that multiply to 12 and add to -8

the two numbers are -2 and -6 because:
-2 + (-6) = -2 - 6 = -8
-2 * -6 = 12

since the leading coefficient is 1, plug the two numbers in factor form

(x - 2) (x - 6)

hope this helps

Answer 5

x^2 - 8x + 12 = (x - 2) * (x - 6)