Factor Theorem
Factor Theorem
Factor Theorem
For a polynomial P(x), if P(a) = 0 then (x − a) is a factor of P(x).
For a polynomial P(x), if P(a) = 0 then (x − a) is a factor of P(x).
Proof
Proof
Since P(a) = 0, the remainder is zero when P(x) is divided by (x − a). (Remainder Theorem)
Since P(a) = 0, the remainder is zero when P(x) is divided by (x − a). (Remainder Theorem)
Therefore, (x − a) is a factor of P(x). (Shown)
Therefore, (x − a) is a factor of P(x). (Shown)