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## How to factor out polynomial into binomials

Ex:

-24x2+48x+74=2
-24x2+48x+72=0
?

Ex:
3x2-30x+65=2
3x2-30x+63=0
?

Hi Cor;
-24x2+48x+72=0
Both coefficients 24 and 48, as well as the constant 72, are multiples of 24.  Henceforth, 24 can be factored out...
-24(x2-2x-3)=0
Let's divide both sides by -24...
[-24(x2-2x-3)]=0/-24
x2-2x-3=0
I did this to illustrate my point that the coefficient of -24 is no longer necessary to resolve this.
Let's factor.
For the FOIL...
FIRST must be (x)(x)=x2
OUTER and INNER must add-up to-2x.
(x-1)(x-1)
Let's FOIL...
FIRST...(x)(x)=x2
OUTER...(x)(-1)=-1x=-x
INNER...(-1)(x)=-1x=-x
LAST...(-1)(-1)=1
x2-x-x+1
x2-2x+1
Obviously, we wanted the constant to be -3, not +1.  The difference is -4...
[(x-1)(x-1)]-4=0
(x-1)2=4
Let's square root both sides..
√[(x-1)2=√4
x-1=2
x=3
Because (x-1)2 has the same result as [-(x-1)2], we must consider such...
-(x-1)=2
-x+1=2
x-1=-2
x=-1

********************************
3x2-30x+63=0
3(x2-10x+21)=0
x2-10x+21=0
(x-7)(x-3)=0
x-7=0
x=7
x-3=0
x=3

(x-1)^2 ≠ [-(x-1)^2]

(x-1)^2 = [-(x-1)]^2