How do you factor 4x212x+9?

2 Answers
Apr 25, 2018

(2x3)(2x3) or (2x3)2

Explanation:

Use the rainbow method.
Multiply the two outer coefficients.
49=36
Find two numbers, that when multiplied equal 36, and when added equal -12.
-6 and -6.
6+6=12
66=36

Rewrite the equation with the x value replaced by the two new values.
4x26x6x+9
Seperate the equation into two parts.
4x26x and 6x+9
Find the GCF of the two parts.
2x(2x3) and 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

4x212x+9=4(x32)2

Explanation:

First, factor x^2

4x212x+9=4(x23x+94)

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

4(x23x+94)=4(x2232x+(32)2)

Last, factor the perfect square trinomial

4(x2232x+(32)2)=4(x32)2