# Math

Can some one explain these to me i need the factors. i am totally lost.
thanks
x^2+x-6
x^2+7x+10
x^2+5x+6
x^2+2xy+15y^2

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1. (x+a)(x+b)
FOIL
x^2 + ax + bx + ab which can be simplified into
x^2 + (a+b)x + ab
Use this as a base for all of the your equations.

Lets do the first one.

ab will be the same as the last term which is -6. Then look at the second term which is x. In this case there is nothing in front of x. However x is the same as 1 times x since 1 times anything is the same. Look back to the equation I gave you.
(a+b)x will be equal to 1x which is equal to x. Therefore, a+b has to equal to 1 and we know ab is equal to -6. List all the two pairs of whole numbers whose product is 6.

1 6
2 3

Since 6 is negative it means one of them has to be negative
-1 6
1 -6
-2 3
2 -3

(a+b) = 1
The only pair of numbers above that add up to 1 is 3 and -2. So just let a = 3 and b = -2.
(x+a)(x+b)
(x+3)(x-2)
And there you go. Sorry, if you still don't understand, I know I'm far from being an expert on explaining stuff.

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2. x^2+7x+10
x^2+(a+b)x+ab
ab = 10
a+b = 7

Pairs whose product is 10.
1 10
2 5

Then only pair that add up to 7 is 2 and 5. So let a = 2 and b = 5.
(x+a)(x+b)
(x+2)(x+5)

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x^2+5x+6
x^2+(a+b)x+ab
ab = 6
a+b = 5

Pairs whose product is 6

1 6
2 3

Then the only pair that adds up to 5 is 2 and 3. So let a = 2 and b = 3.
(x+a)(x+b)
(x+2)(x+3)

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The last one is complicated... and it involves material that you may not have learned yet if you just started factors. Are you sure it is correct?

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