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Question
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Options
f(x) g(x)
−f(x) + g(x)
f(x) − g(x)
\[\left\{ f(x) + g(x) \right\} g(x)\]
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Solution
As (x -1)is a factor of polynomial f(x) but not of g(x)
Therefore f(1) = 0
Now,
Let p(x) = f(x).g(x)
Now
`p(1) = f(1) .g(1)`
`p(1) = 0 0.g(1)`
` = 0`
Therefore (x − 1) is also a factor of f(x).g(x).
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