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.

need more info

step-by-step explanation:

what do you mean by "representation"? graph? table? etc.