If a polynomial is divided by x minus 5, the quotient is 2 x squared plus 7 x minus 7 and the remainder is 7. find the original polynomial.

The original polynomial is .

Step-by-step explanation:

The division of polynomial is analogue to the division of integers or natural numbers. For example, if we divide 25 by 6, we obtain that 4 is the quotient and the remainder is 1. We can recover 25 as 25 = 6*4+1.

Then, with this particular case, if we denote by P(x) the original polynomial, we have:

Expanding the above multiplication:

In general, given a polynomial P(x), if we divide it by another polynomial Q(x) (the divisor), there exist polynomials S(x) (the quotient) and R(x) (the remainder) such that

P(x) = Q(x)S(x) + R(x).

because they could drop even lower..