Perfect+Square+Trinomials

Perfect Square Trinomial

A Perfect Square Trinomial is a quadratic equation that as its first and last terms perfect squares. Factoring these are simple. You get the square root of the first number and put that as the first term in the parenthesis. Then, you look and see if the first sign is addition or subtraction. You then plug that in. Finally, you get square root of the second number and put that as the final term. This may sound confusing but a few examples should help.

__First Example__

4x 2 +16x+16

First thing is you have to take out the GCF.

4(1x 2 +4x+4)

Next, you get the square roots of 1 and 4. The square root of 1 is 1, and the square root of 4 is 2. After you get that you look at the first addition/subtraction sign. It is a "+" so you put a "+" in the parenthesis.

4(x+2)(x+2)

Afterwards, you can simplify it

** 4(x+2) 2 **

__ Second Example __

2) 9x 2 +30x+25

There is no GCF, so we can continue to factor as normal. The square root of 9 is 3 and the square root of 25 is 5.

(3x+5)(3x+5)Simplifies to...

**(3x+5) 2 ** **//__ REMEMBER: __//** The linear term (the middle number) sometimes may cause the quadratic not to be a perfect square trinomial. For example: 4x 2 +9x+100. The first and the last numbers are perfect squares so you would do (2x+10)(2x+10). But after FOIL'ing that out you get 4x 2 +40x+100.