Question

The quotient, when $5x^2+3$ is divided by $\frac{1}{x}+2$ is

• A. $\frac{20x^2-10x+17}{4}$
• B. $\frac{5x^2-5x+17}{8}$
• C. $\frac{20x^2-10x+17}{8}$
• D. $\frac{5x^2-5x+17}{4}$

Answer 1

The correct option is C $\frac{20x^2-10x+17}{8}$

$\text{Polynomial,}P\left(x\right)=5x^2+3\text{Divisor,}d\left(x\right)=\frac{1}{x}+2=\frac{2x+1}{x}\text{We can simplify the division}\frac{5x^2+3}{\frac{2x+1}{x}}=\frac{5x^2+3}{2x+1}\times x=\frac{5x^3+3x}{2x+1}2x+1)5x^3+3x(\frac{5}{2}{x}^2-\frac{5}{4}x+\frac{17}{8}\underset{–}{{}_{-}5x^3\pm \frac{5}{2}{x}^2}\frac{5x^3}{2x}=\frac{5x^2}{2}\underset{–}{-\frac{5}{2}{x}^2+3x\mp \frac{5}{2}{x}^2\mp \frac{5}{4}x}\frac{-\frac{5x^2}{2}}{2x}=-\frac{5x}{4}\underset{–}{\frac{17}{4}x{}^{}{}_{-}\frac{17}{4}x\pm \frac{17}{8}}\frac{\frac{17}{4}x}{2x}=\frac{17}{8}-\frac{17}{8}\text{The quotient is:}\frac{5x^2}{2}-\frac{5x}{4}+\frac{17}{8}=\frac{20x^2-10x+17}{8}$