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Question
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
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Solution
According to the question,
Let p(x) = 4x2 + x − 2 and g(x) = x – 2
g(x) = x – 2
Zero of g(x)
⇒ g(x) = 0
x – 2 = 0
x = 2
Therefore, zero of g(x) = 2
So, substituting the value of x in p(x), we get,
p(2) = 4(2)2 + 2 − 2
= 16 ≠ 0
Since, the remainder ≠ zero,
We can say that,
g(x) = x – 2 is not a factor of p(x) = 4x2 + x − 2
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