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Question
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
Solution
According to the question,
g(x) = 2x + 1
Then, zero of g(x),
g(x) = 0
2x + 1 = 0
2x = –1
x = `-1/2`
Therefore, zero of g(x) = `-1/2`
So, substituting the value of x in p(x), we get,
`p(-1/2) = 2 xx (-1/2)^3 - 11 xx (-1/2)^2 - 4 xx (-1/2) + 5`
= `-1/4 - 11/4 + 7`
= `16/4`
= 4 ≠ 0
Hence, p(x) is not the multiple of g(x), the remainder ≠ 0.
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