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How do you factor #3x^3 - 2[ x - ( 3 - 2x ) ] = 3 ( x - 2 )^2#?

Answer 1

Abigail Allen

The factored form is #3(x^2+2)(x-1)=0#.

#3x^3-2[color(blue)(x-(3-2x))]=3color(red)((x-2)^2)#

#3x^3-2[color(blue)(x-3+2x)]=3color(red)((x^2-4x+4))#

#3x^3-2[color(blue)(3x-3)]=color(red)(3x^2-12x+12)#

#3x^3-color(blue)(6x+6)=color(red)(3x^2-12x+12)#

#3x^3-3x^2+6x-6=0#

#3x^2(x-1)+6(x-1)=0#

#(3x^2+6)(x-1)=0#

#3(x^2+2)(x-1)=0#

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Answer 2

Abigail Allen

To factor the expression (3x^3 - 2[ x - ( 3 - 2x ) ] = 3 ( x - 2 )^2), you would first simplify the expression within the brackets. Then, you can proceed to expand the squared binomial on the right-hand side of the equation and simplify it further. Once you have simplified both sides, you can compare the terms to identify the factors on the left-hand side of the equation.

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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.