Forming a Cubic Polynomial with Known Remainders and Roots

STRUCTUREDMedium

Question

A quadratic polynomial $G(x)$ has remainders $\frac{1}{3}$ , $\frac{1}{5}$ , and $\frac{1}{8}$ when divided by $(x - 1)$ , $(x - 3)$ , and $(x - 6)$ respectively. Show that $(x - 1)$ , $(x - 3)$ , and $(x - 6)$ are factors of the polynomial

f(x) = (x + 2)G(x) - 1

Hence, find $f(x)$

PolynomialsRemainder TheoremPartial Fractions

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