Factor Theorem with Proof and Examples

Home Previous Question Next Question Factor Theorem : If (p(x)) is a polynomial of degree (n geq 1) and (a) is any real number, then (x-a) is a factor of (p(x)), if  and only if (p(a)=0). Proof: By the Remainder Theorem, (p(x)=(x-a) q(x)+p(a)).(i) If (p(a)=0), then (p(x)=(x-a) q(x)), which shows that (x-a) is a factor

Remainder Theorem with Proof and Examples

Home Previous Theorem Next Theorem Remainder Theorem : Let (p(x)) be any polynomial of degree greater than or equal to one and let a be any real number. If (p(x)) is divided by the linear polynomial (x-a), then the remainder is (p(a)). Proof : Let (p(x)) be any polynomial with degree greater than or equal

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