Math
posted by joyce on .
Can some one explain these to me i need the factors. i am totally lost.
thanks
x^2+x6
x^2+7x+10
x^2+5x+6
x^2+2xy+15y^2

(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)(x2)
And there you go. Sorry, if you still don't understand, I know I'm far from being an expert on explaining stuff. 
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?