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Question
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
Solution
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
To check whether x - 2 is a factor of p(x) now put x = 2 in equation (i), we get
p(2) = (2)3 - 3(2)2 + 4(2) -4
= 8 - 3 x 4 + 8 - 4
= 8 - 12 + 8 - 4
= 16 - 16 = 0
Since, p(2) = 0, so by factor theorem (x - 2) is a factor of p(x).
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