SOLUTION: 9. Using Factoring, how do I complete this exercise? 25x^2 + 20x + 4 thank you!

Question 156565: 9. Using Factoring, how do I complete this exercise?
25x^2 + 20x + 4
thank you!
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
None of the coefficients have anything in common besides 1. So, we are going to need a 5 coefficient for a,c in (ax+b)(cx+d) factorization.
So we need (5x+b)(5x+d)=25x^2+20x+4. We can suspect b=d=2 because if b=4, our x coefficient becomes >20. So (5x+2)^2 is our factorization.
Now, we could solve this slightly differently, yet more concisely:

(5x+b)(5x+d)=25x^2+20x+4
25x^2+5xd+5xb+bd=25x^2+20x+4

This means that:
5d+5b=20
bd=4
from the first equation: d=4-b
putting that into the second equation: b(4-b)=4
4b-b^2-4=0
b^2-4b+4=0
We must necessarily have solution b=2 and d=4-2=2 as well. So we place those values in our hybrid form, getting the answer already supplied.
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