Factor the expression below why explain why.

54.

-2h^2 + 4h + 70

-2 (h+5) (h-7)

Take out the GCF: - 2 (h^2-2h-35)

You want to find the factors of - 35 that add to get - 2

Those numbers would be 5 and - 7 since they multiply to get - 35 and add to get you - 2

A quadratic has the form ax^2+bx+c

To factor a quadratic you want to find two values, j and k, which satisfy two conditions ...

j*k=a*c and j+k=b

In this case ac=-140 and b=4.

The only values possible are j=14 and k=-10

so jk=-140 and j+k=4 which are the conditions we needed to satisfy ...

Now you remove the linear, or "b term", from the original equation and replace it with jx and kx ... and in this case you will have:

-2h^2-14h+10h+70 now you can factor out the greatest common factor from the first pair of terms and the second pair of terms ...

-2h (h+7) + 10 (h+7) which is equal to

(-2h+10) (h+7) and you can factor the first term again if you wish ...

-2 (h-5) (h+7)