Question

If f(x) is a polynomial such that f(a) = f($\frac{b}{2}$) = f($\frac{c}{3}$) = 0, then which of the following expressions is a factor of f(x)

Answer 1

Suppose f(x) is a polynomial. Also, if f($\frac{p}{q}$) = 0, then, we can write, f(x) = (x – $\frac{p}{q}$) g(x), for some polynomial g(x).

i.e. f(x) = (qx – p).($\frac{g\left(x\right)}{q}$) = (qx – p) h(x), for some polynomial h(x) = $\frac{g\left(x\right)}{q}$.

So, if f(p/q) = 0 , then (qx – p) is a factor of f(x).