How do you factor???

Question

how do you factor 4x^2-24x+36


please someone help me

Answer 1

Hopefully, this helps. My algebra teacher called this method the "Super Diamond."

To begin with, the problem is written in the form ax^2 + bx + c. If "a" doesn't equal 1 (as is in your case), multiply "a" and "c" together. Now, draw an X. Put the product of "a" and c" in the top section of your X, and put "b" in the bottom section of your X. Think of 2 numbers that multiply to equal that number and add to equal "b." Put the two numbers on the side sections of the X. So, for your problem your X would have 144 on the top, 24 on the bottom, and 12 on both sides, because 12 times 12 = 144 and 12 + 12 = 24. Use the 2 numbers in your factoring. Because "a" is not 1, you must include it in your factoring:

(4x + 12)(4x + 12)
This can be reduced to: (x + 3)(x + 3), which can be further simplified to (x + 3)^2. And there is your fully-factored form!

Hope it makes sense, and good luck! :)

Answer 2

method 1
4x^2-24x+36 = (2x)^2-2.2x.6+(6)^2
this is of the form (a^2-2.a.b+b^2) = (a-b)^2
which gives us (2x-6)^2 = 2^2(x-3)^2 = 4(x-3)^2
method 2
from 4x^2-24x+36 take common factor 4 out.
which gives us 4(x^2-6x+9) = 4(x^2-2.3.x+3^2) = 4(x-3)^2
method 3
multiply 4 and 36, we get 144.
now -12x-12x = -24x and -12x X -12x = -144x
there4, 4x^2-24x+36 = 4x^2-12x-12x+36 = 4(x^2-3).4(x^2-3)
= 4(x^2-3)
i have done all three methods just to prove that my answer is correct.Choose whichever method u find easy. bye.....

Answer 3

4x^2-24x+36
first factor out the 4
(4)(x^2-6x+9)
now it's easier to work with
Not much goes into 9...only 1,3,9...so assuming this will be easy lets go with 3
(4)(x-3)(x-3)

Answer 4

You factor out the 4:
4(x^2 - 6x + 9)

Then you factor the inside:
(x - 3)(x - 3) or (x - 3)^2

Then you're done!

Multiply it back together to check if you foiled correctly.

Answer 5

4 x^2-24x+36=0

4(x^2-6x+9)=0
4(x-3)(x-3)=0

x=3

Answer 6

(2x-6)(2x-6)