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)

• \[\left\{ f(x) + g(x) \right\} g(x)\]

Answer 1

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).