Question

x-3 is a factor of P(x)=x³-7x²+15x-9

a. true
b. false

Answer 1

a

Answer 2

as f(3) = 0

Answer 3

In general, if x-r is a factor of P(x), then P(r) = 0


So simply plug in x = 3 (because here r = 3) and evaluate


\[\Large P(x) = x^3-7x^2+15x-9\]


\[\Large P(3) = (3)^3-7(3)^2+15(3)-9\]


\[\Large P(3) = 27-7(9)+15(3)-9\]


\[\Large P(3) = 27-63+45-9\]


\[\Large P(3) = 0\]


Because P(3) = 0, this means that x-3 is indeed a factor of P(x)