Show that 3p² + 4q = 0, if x² + px + q and 3x² + q have a common factor x -b | Polynomials

Given that x² +px+q and 3x² + q have a common factor x - b, where p, q and b are nonzero, show that: 3p² +4q = 0
Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x - a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a). So basically, x -a is the divisor of P(x) if and only if P(a) = 0. It is applied to factorize polynomials of each degree in an elegant manner.