If m and n are the polynomials of x^2-7x+c, such that m-n=1 then find the value of c

Answer 1

I think you mean that M and N are factors of the polynomial x²-7x+c, right?

Since we don't know c, the only thing we DO know is that the constant element of the two factors must add up to -7. So what pair of constants will add to -7 and have the whole factors subtract (as in the instruction m-n) to 1. Those numbers would be -3 and -4 *in that order*. So your factors would be m= (x-3) and n=(x-4) because (x-3) - (x-4) = 1. You can then FOIL (distribute) to get the c term as (-3) times (-4) = 12.

Best wishes