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 + 2

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

x + 2 = 0


⇒ x = – 2


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


3(– 2)3 – (– 2)2 – 3(– 2) + 1 = – 24 – 4 + 6 + 1


= – 21


⇒ Remainder = – 21≠0


⇒ g(x)) = x + 2 is not a factor of p(x) = 3x3 – x2 – 3x + 1.


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