The quotient- when 5 x2-3 is divided by 1-x-2 isA- 20 x2-10 x-17-4B- 5 x2-5 x-17-8C- 20 x2-10 x-17-8D- 5 x2-5 x-17-4

The correct option is C 20x^2 nbsp; 10x+17 8Polynomial, P(x) = 5x^2+3 Divisor, d(x) =1 x+2 nbsp; = 2x+1 x We can simplify the division 5x^2+3 nbsp; ...

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Standard X

Mathematics

Division Algorithm for a Polynomial

The quotient,...

Question

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

\frac{20 x^{2} - 10 x + 17}{4}

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\frac{5 x^{2} - 5 x + 17}{8}

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\frac{20 x^{2} - 10 x + 17}{8}

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\frac{5 x^{2} - 5 x + 17}{4}

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Solution

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

Suggest Corrections

The quotient, when 5x2+3 is divided by 1x+2 is

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