Q2 of 90 Page 31

Use the factor theorem to determine whether g(x) is a factor of p(x)?

p(x) = 3x3 – x2 – 3x + 1; g(x) = x + 1

Substituting the g(x) = 0, we get -

x + 1 = 0


⇒ x = – 1


Now, substituting x = – 1 in p(x), we get -


3(– 1)3 – (– 1)2 – 3(– 1) + 1 = – 3 – 1 + 3 + 1


= 0


⇒ Remainder = 0


⇒ g(x) = x + 1 is a factor of p(x) = 3x3 – x2 – 3x + 1.


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