If on division of a non - zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degree of p (x) and g (x)?

Question

Philoid · Accepted Answer

g(x) is the factor of p(x) and degree of p(x) degree of g(x)

Here r(x) = 0

By division algorithm,

p(x) = g(x)q(x) + r(x)

p(x) = g(x) q(x)

∴ deg(p(x)) = deg(g(x))×deg(q(x))

⇒ deg(p(x))≥ deg(g(x))

Hence g(x) is the factor of p(x) and clearly degree of p(x) degree of g(x)