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How do you factor #12x²-24x+9#?

Answer 1

Ethan Adkins

#12x^2-24x+9 = 3(2x-1)(2x-3)#

First separate out the common scalar factor #3#:

#12x^2-24x+9 = 3(4x^2-8x+3)#

To factor the remaining quadratic #4x^2-8x+3# use an AC method:

Find a pair of factors of #AC = 4*3=12# with sum #B=8#

The pair #6, 2# works.

Use this pair to split the middle term and factor by grouping:

#4x^2-8x+3 = 4x^2-6x-2x+3#

#color(white)(4x^2-8x+3) = (4x^2-6x)-(2x-3)#

#color(white)(4x^2-8x+3) = 2x(2x-3)-1(2x-3)#

#color(white)(4x^2-8x+3) = (2x-1)(2x-3)#

Putting it all together:

#12x^2-24x+9 = 3(2x-1)(2x-3)#

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Answer 2

Eva Adamson

To factor ( 12x^2 - 24x + 9 ), you can use the factoring method for trinomials. Start by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 3. Then, rewrite the trinomial in the form ( ax^2 + bx + c ), where ( a = 12 ), ( b = -24 ), and ( c = 9 ). Next, factor the trinomial using the appropriate method, such as factoring by grouping or using the quadratic formula. Once factored, the expression will be in the form ( (mx - p)(nx - q) ), where ( m ), ( n ), ( p ), and ( q ) are constants.

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Answer from HIX Tutor

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