FACTORS OF A POLYNOMIAL
Polynomial of Class 9
FACTORS OF A POLYNOMIAL
Statement: If P(x) is a polynomial of degree n≥1 and a is any real number, then (i)x-a is a factor of p(x), if p(a)=0 and (ii) p(a)=0 if x-a is a factor of p(x)
Proof: By the Remainder Theorem we have, p(x)=(x-a)q(x) +p(a)
(i) If p(a)=0, then p(x)=(x-a)q(x) which indicates that x-a is a factor of p(x),
(ii) Since x-a is a factor of p(x),p(x)=(x-a) g(x) for some polynomial g(x) In this case, p(a) = (a-a)g(a) = 0.
