factor math problem?

6(X^2+X-2)
6(X+2)(X-1)

6x^2+6x-12=
6(x^2+x-2) =
6(x+2)(x-1)

1. Factor completely: x^2 + 10x + 25 A) (x + 5)(x - 5) B) (x + 5)(x + 5) C) (x - 5)(x - 5) D) (x + 25)(x + 1) Answer is B. x*x =x^2; 5*5=25; 5*x+5*x =10x 2. Factor completely: 3x^2 - 12 A) 3(x^2 - 4) B) 3(x + 2)(x + 2) C) 3(x + 2)(x - 2) D) (x + 2)(x - 2) Answer is C. A is correct but did not go far enough. x^2-4 can be factored to (x+4)(x-4). 3. Factor completely: 2x^2 - x - 10 A)(2x - 5)(x + 2) B) (2x + 5)(x - 2) C) (2x + 5)(x + 2) D) (2x - 5)(x - 2) Answer is A. 2x*x =2x^2; (-5)(2)=-10;(-5)x +(2x)2 = -x 4. Simplify completely: (4x -8) / (x-2) A) 4(x-2) / (x-2) B) 4 C) 8 D) 3x+4 Answer is B. A did not cancel the x-2 terms to get 4. It should that x cannot be equal to 2 or you would be dividing by zero which is a no-no

6x^2 + 6x - 12
= 6(x^2 + x - 2)
= 6(x + 2)(x - 1)

multiply 6x^2 wid -12 and resolve it into factors
since 6x^2* -12 = - 72x^2
resolve it into factors in such a way that the factor pair when multiplied or subtracted should give the rsult of 6x
factors of 72 are ( keep x^2 aside to avoid confusion anduse
1*72 later ven u get the factors)
2*36
3*24
4*18
6*12
8*9 and .......................................

now use this factor pair and add or subtract it to get 6x
the pair 6*12 can solve this
now use the term x^2
12x - 6x
here the term minus is used because 6x^2* -12 is - 72x^2
so here when we multiply the factors we should get - 72x^2 and when we add or subtract we should get +6x
the factorise is given by
6x^2+12x-6x-12
divide into two terms
(6x^2+12x)+(-6x-12)
take 6x common in the first term
6x(x+2)
and now take -6 common in the second term
-6(x+2)
therfore 6x(x+2)-6(x+2)
now the answer is
(x+2) (6x-6)

Yes it can be factored.

6 x -12 = -72
-6 + 12 = 6

6x^2 - 6x + 12x - 12

6(x^2 - x + 2x - 2)

6[(x(x-1) +2(x-1)]

6(x+2)(x-1)

6x^2+6x-12
6(x^2+x-2)
6(x^2-x+2x-2)
6(x{x-1}+2{x-1})
6({x+2}{x-1})
6(x+2)(x-1)

6(x^2 + x - 2)