Year 11 Maths - Methods Polynomials

Division Of Polynomials

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Questions

Question 1

28642

\(\dfrac{{2x - 1}}{{x + 4}} = \,\,\,?\)

\(2 - \dfrac{9}{{x + 4}}\)

\(1 - \dfrac{2x}{{x + 4}}\)

\(2 - \dfrac{6}{{x + 4}}\)

\(1 - \dfrac{x}{{x + 4}}\)

Answer

\(2 - \dfrac{9}{{x + 4}}\)

Worked Solution

\begin{align}
&\begin{aligned}
&\qquad 2\\
x+4&\sqrt{2x-1}\\
&\quad \underline{2x+8}\\
&\qquad -9\\
\end{aligned}\\
&\begin{aligned}
\therefore 2x-1&=2(x+4)-9\\
\frac{2x-1}{x+4}&=\frac{2(x+4)}{x+4}-\frac{9}{x+4}\\
&=2-\frac{9}{x+4}\qquad \therefore A
\end{aligned}\\
\end{align}

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