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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 + x2 + 3x + 175 and g(x) = x + 5.
Solution
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5 ...(i)
To check whether (x + 5) is a factor of p(x), we have to find p(-5), put x = -5 in equation (i), we get
p(-5) = (-5)3 + (-5)2 + 3(-5) + 175
= -125 + 25 - 15 + 175
= -140 + 200 = 60
Since, p(-5) ≠ 0, so by factor theorem (x + 5) is not a factor of p(x).
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