How do you factor #4x^2-12x+9#?

2 Answers
Phiri
Apr 25, 2018

#(2x-3)(2x-3)# or #(2x-3)^2#

Explanation:

Use the rainbow method.
Multiply the two outer coefficients.
#4 * 9 = 36#
Find two numbers, that when multiplied equal 36, and when added equal -12.
-6 and -6.
#-6 + -6 = 12#
#-6 * -6 = 36#

Rewrite the equation with the x value replaced by the two new values.
#4x^2 -6x - 6x + 9#
Seperate the equation into two parts.
#4x^2 -6x# and #-6x +9#
Find the GCF of the two parts.
#2x(2x - 3)# and #-3(2x-3)#

Take the GCF as your first factor, and the two remaining values as the second.
2x-3 and 2x-3

Vicente P.
Apr 25, 2018

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

Explanation:

First, factor x^2

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

Then, identify the y element in the form #(x+y)^2 = x^2 + 2xy + y^2#

#4(x^2 - 3x + 9/4) = 4(x^2 -2*3/2 x + (3/2)^2)#

Last, factor the perfect square trinomial

# 4(x^2 -2*3/2 x + (3/2)^2) = 4(x-3/2)^2#

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