Posted by **joyce** on Monday, March 31, 2008 at 12:12am.

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

- Math -
**Anonymous**, Monday, March 31, 2008 at 12:34am
(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.

- Math -
**Anonymous**, Monday, March 31, 2008 at 12:45am
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)

-----------------------------

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)

-----------------------------

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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