How do you factor #3(x-2) - 4x(2-x)#?

Answer 1

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

Factor a #-1# term out of the #(2-x)#. This will turn it into #-(x-2)#.

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

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

Now, this resembles what would come out of a factor by grouping problem. Notice how the #(x-2)# term is common to both the #3(x-2)# and the #4x(x-2)#.

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

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Answer 2

Julia Adams

To factor (3(x-2) - 4x(2-x)), you first distribute each term inside the parentheses:

[3(x-2) = 3x - 6] [4x(2-x) = 8x - 4x^2]

Then, combine like terms:

[3x - 6 - (8x - 4x^2)]

[= 3x - 6 - 8x + 4x^2]

[= (3x - 8x) + 4x^2 - 6]

[= -5x + 4x^2 - 6]

So, the factored expression is (-5x + 4x^2 - 6).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.