Given that a cubic polynomial $\mathrm{f}\left( x \right)$ has a factor $x$ and \(\mathrm{f}\lef

Question

Given that a cubic polynomial $\mathrm{f}\left( x \right)$ has a factor $x$ and $\mathrm{f}\left( x+1 \right)-\mathrm{f}\left( x \right)=3{{x}^{2}}+7x$, by substituting suitable values of $x$, show that $\mathrm{f}\left( x \right)$ has a factor of $x-1$, show that $\mathrm{f}\left( x \right)$ has a remainder of $10$ when it is divided by $x-2$, find the remainder when $\mathrm{f}\left( x \right)$ is divided by $x+1$. Find $\mathrm{f}\left( x \right)$

Accepted Answer

(a)(i) Factor $x-1$ (a)(ii) Remainder $10$ (a)(iii) $f(-1)=4$ (b) $f(x)=x(x-1)(x+3)$

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

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