how do you factor 3(x-2)^2 -3(x-2)-6?

Answer 1

Let t = (x-2)

3t^2 - 3t - 6
3(t^2 - t - 2)
3(t - 2)(t + 1)

Then substitute x-2 back in:

3(x - 2 - 2)(x - 2 + 1)
3(x - 4)(x - 1)

Answer 2

3 [ (x - 2) ² - (x - 2) - 2 ]
Let y = (x - 2)
3 [ y ² - y - 2 ]
3 (y - 2) (y + 1)
3 (x - 4) (x - 1)

Answer 3

let y = (x-2)

3(x-2)^2 - 3(x-2) -6
replace (x-2) in the above equation by y.
hence, we have 3y^2 - 3y -6 = (3y-6)(y+1)
= [ 3(x-2) -6] [(x-2)+1]
= [ 3x -6 -6] [ x-2+1]
= (3x-12) (x -1)
=3(x - 4) (x-1)

Answer 4

3(x-2)^2 -3(x-2)-6

Substitute y = x - 2

3y^2 - 3y - 6

3(y^2 - y - 2)

3(y - 2)(y + 1)

3(x - 2 - 2)(x - 2 + 1) {replace y}

3(x - 4)(x - 1)

Answer 5

3(x-2)^2 -3(x-2)-6
3[ (x-2)^2 -(x-2) -2 ]
3[ x^2 -4x +4 -x +2 -2]
combine similar terms
3[x^2 -5x +4]
3(x -1)(x -4)

Answer 6

its easy folly this rule P. E.M.D.A.S. follow this formula always
P=parentheses
E=exponents
M=multiply
D=divide
A=add
S=subtract