Factor each Polynomial Completely

Hi there,

I have solved this problem wana make sure from you guys i have solved it correctly or not please see below. Thanks!

Factor each Polynomial Completely:

4x^2 - 20x + 25
= 4(x^2 - 5x + 25)
= 4(x - 5)^2

One quick way to tell if you have done it correctly is to plug in a few values for x and see if the first formula equals the last.
Good thing to try is usually x = 0, -1, and 1.
4x^2 - 20x + 25
4(0)^2 - 20(0) + 25 = 25

4(x - 5)^2
4(0-5)^2 = 4*25 = 100
Oops, they don't agree so you know it is wrong.
You didn't factor a 4 out of 25. If you look at your middle one and multiply it back in you get
4x^2-20x+100.

4x^2 - 20x + 25
The factors of 25 are 1,5 and 25
The factors of 4 are 1,2 and 4
If the factors are integers the only possiblites are
(4x-1)*(x-25)
(4x-25)*(x-1)
(4x-5)*(x-5)
(2x-25)*(2x-1)
(2x-5)*(2x-5)
They are the only ways the multipliers of x = 4 and the constant multipliers = 25
All you have to do is check which one gives -20 for the middle term.

Thank you Gene!


This is really help I got it correct answer is (2x-5)^2, Right?

Again nice explanation!

Right on.
Note that
(0-5)^2 = 25
as required. I should mention that for a second degree equation you should plug in three easy numbers for a complete verification. If three numbers give a match you are certain that it is correct. Two might match by rare bad luck. Of course if any don't match you have an error.
-------------------
Gene

Thanks Again!