When factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten

 -7x should be written as -15x+8x or 8x-15x

Explanation:

Multiply the first coefficient 6 and the last term -20 to get -120

We need to find factors of -120 that add to the middle coefficient -7

Through trial and error you should find that

-15 + 8 = -7

-15 * 8 = -120

Therefore, we break the -7x into -15x+8x

Extra info: if you want to fully factor by grouping, then follow these steps

6x^2 - 7x - 20

6x^2 - 15x + 8x - 20 ... break up -7x

(6x^2 - 15x) + (8x - 20) group into pairs

3x(2x - 5) + 4(2x - 5) factor each group

(3x + 4)(2x - 5) pull out the overall GCF 2x-5

So 6x^2-7x-20 fully factors to (3x+4)(2x-5)

We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.

-50/3 is the final answer! : )