Factorise: 2(x-4)-3(x-4)^2?

2(x-4)-3(x-4)²
Common factor = (x - 4). Factor it out
= (x - 4)(2 - 3(x - 4))
= (x - 4)(2 - 3x + 4)
= (x - 4)(6 - 3x)
= 3(x - 4)(2 - x)
That is now completely factored.

Factorise:

2(x - 4) - 3(x - 4)^2

Factor out the Greatest Common Factor (GCF) of (x - 4) from each term in the polynomial

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

Factor out the GCF of (x - 4) from

2(x - 4) - 3(x - 4)^2

(x - 4) (2 - 3(x - 4)

Multiply -3 by each term inside the parentheses.

(x - 4) (2 - 3x + 12)

Add 12 to 2 to get 14

(x - 4) (14 - 3x)

Reorder the polynomial 14 - 3x alphabetically from left to right, starting with the highest order term.

(x - 4) (-3x + 14)

The answer is:

(x - 4) (-3x + 14)

(x - 4) [ 2 - 3 (x - 4) ]

(x - 4) [ 14 - 3x ]

take (x-4) common to get
(x-4)(2 - 3(x-4))

simplify to get

(x-4)(2-3x+8) = (x-4)(10-3x)

2(x - 4) - 3(x - 4)^2
= (x - 4)[2 - 3(x - 4)]
= (x - 4)(2 - 3x + 12)
= (x - 4)(-3x + 2 + 12)
= (x - 4)(-3x + 14)

2(x-4)-3(x-4)^2
= 2x -- 8 -- 3(x^2 -- 8x + 16)
= 2x -- 8 -- 3x^2 + 24x -- 48
= -- 3x^2 + 26x -- 56
= -- 3x^2 + 12x + 14x -- 56
= -- 3x(x -- 4) + 14(x -- 4)
= (x -- 4)(14 -- 3x)