How do you factor 4x^2-12x+94x212x+9?

2 Answers
Apr 25, 2018

(2x-3)(2x-3)(2x3)(2x3) or (2x-3)^2(2x3)2

Explanation:

Use the rainbow method.
Multiply the two outer coefficients.
4 * 9 = 3649=36
Find two numbers, that when multiplied equal 36, and when added equal -12.
-6 and -6.
-6 + -6 = 126+6=12
-6 * -6 = 3666=36

Rewrite the equation with the x value replaced by the two new values.
4x^2 -6x - 6x + 94x26x6x+9
Seperate the equation into two parts.
4x^2 -6x4x26x and -6x +96x+9
Find the GCF of the two parts.
2x(2x - 3)2x(2x3) and -3(2x-3)3(2x3)

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

Apr 25, 2018

4x^2 - 12x+ 9 = 4(x-3/2)^24x212x+9=4(x32)2

Explanation:

First, factor x^2

4x^2 - 12x + 9 = 4(x^2 - 3x + 9/4)4x212x+9=4(x23x+94)

Then, identify the y element in the form (x+y)^2 = x^2 + 2xy + y^2(x+y)2=x2+2xy+y2

4(x^2 - 3x + 9/4) = 4(x^2 -2*3/2 x + (3/2)^2)4(x23x+94)=4(x2232x+(32)2)

Last, factor the perfect square trinomial

4(x^2 -2*3/2 x + (3/2)^2) = 4(x-3/2)^24(x2232x+(32)2)=4(x32)2