Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the divisor

Question

Divided:5x^3+x^2+3 ,quotient:5x^2-14x+42, remainder:-123

Answer 1

we know that

5x^3+x^2+3 = p(x)*(5x^2-14x+42) - 123
so,
5x^3 + x^2 + 126 = p(x)*(5x^2 - 14x + 42)

a simple long division yields p(x) = (x+3)