How do you factor quadratic equations

The problem that I'm having the most difficulty with is x²+7x+10=0.

(x + 5)(x +2)

You begin by making two open sets of parenthesis: ( )( )

Obviously, since the first thing in the problem is X^2 then you know this means X times X so it goes in the first position in both equations. (x )(x )

Now you have to determing what are the factors of +10? (two numbers multiplied that = 10)

Factors of 10 are 1x10, 2x5

Of these two selections which set added or subtracted from one another can = the middle term (7)?

2 + 5 Right?

So...

(x + 2)(x + 5)

Hope this helps.

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Ok, so you need to yet two numbers that multiply to make the last number (10) and ALSO add to make the number before x (7), and then put those two numbers into two brackets (no need to worry about signs because there are no negatives. The two numbers are 2 and 5 (x+2)(x+5). You will notice if you multiply it out it will be the equation you started with.

solve for x using the formula for quadratic equations. in this case x = -5 and x = -2

use this algorithm for factorization:

a*(x-solution1)(x-solution2)

where a is in ax²+sx+c (this case a=1)

(x-(-5))(x-(-2)) = (x+5)(x+2)

To Factor x²+7x+10=0.

You have to ask yourself:
--which two numbers multiply to give 10
--which also add up to 7

those two numbers are 5 and 2

Answer : (x+2)(x+5)

(x+2)(x+5)