Question 686974
Given: {{{4X^2 + 10X + 4}}}

If you factor a 2 out of each number, the equation can be written as:
{{{2*(2X^2 + 5X + 2)}}}

You need to remember to multiply the equation by 2 later but lets just look at the {{{2X^2 + 5X + 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^2 + 5X + 2 = (2X + 1)*(X + 2)}}}

Now we have to multiply that equation by 2 since we divided it by 2 in the first place.
{{{highlight(2*((2X + 1)*(X + 2)))}}}
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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)

{{{(2X + 1)*(X + 2) = (2X*X) + (2X*2) +  (1*X) + (1*2)}}}
Simplify
{{{2X^2 + 4X + 1X + 2}}}
Combine like terms
{{{2X^2 + 5X + 2}}}
Now multiply that by the 2
{{{2*(2X^2 + 5X + 2) = 4X^2 + 10X + 4}}}