SOLUTION: I don't understand how to find the factors for this equation : 4x to the second power + 10x + 4= The answer is 2(2x to the second power + 5x + 2) = 2(2x + 1)(x+2

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I don't understand how to find the factors for this equation : 4x to the second power + 10x + 4= The answer is 2(2x to the second power + 5x + 2) = 2(2x + 1)(x+2      Log On


   



Question 686974: I don't understand how to find the factors for this equation : 4x to the second power + 10x + 4=
The answer is 2(2x to the second power + 5x + 2)
= 2(2x + 1)(x+2)
I understand the first problem, but I don't see the 10x in the final solution. I don't understand why this is the answer.

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 4X%5E2+%2B+10X+%2B+4
If you factor a 2 out of each number, the equation can be written as:
2%2A%282X%5E2+%2B+5X+%2B+2%29
You need to remember to multiply the equation by 2 later but lets just look at the 2X%5E2+%2B+5X+%2B+2 portion right now.
Find the factors of the last 2 in the equation: 1 & 2
Find the factors of 2X^2: 1X & 2X
Now since the last 2 is positive that means that both factors contain both + signs or both - signs.
But since the 5X is positive, both factors can not contain negative signs.
Then you have to see which of your factors fit.
2X%5E2+%2B+5X+%2B+2+=+%282X+%2B+1%29%2A%28X+%2B+2%29
Now we have to multiply that equation by 2 since we divided it by 2 in the first place.
highlight%282%2A%28%282X+%2B+1%29%2A%28X+%2B+2%29%29%29
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You can always double check your answer by goin backwards and making sure you get what you started with.
Use the foil method on the inside of the parentheses.
(FOIL = first, outer, inner last)

Simplify
2X%5E2+%2B+4X+%2B+1X+%2B+2
Combine like terms
2X%5E2+%2B+5X+%2B+2
Now multiply that by the 2
2%2A%282X%5E2+%2B+5X+%2B+2%29+=+4X%5E2+%2B+10X+%2B+4