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Definition of Function

If A=2x3+5x...

Question

If $A = 2 x^{3} + 5 x^{2} + 4 x + 1$ and $B = 2 x^{2} + 3 x + 1$ , then find the quotient from the following four option, when A is divided by B.

A

x - 1

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B

x + 1

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C

2 x + 1

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D

2 x - 1

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Solution

The correct option is B $x + 1$
$\frac{A}{B} = \frac{2 x^{3} + 5 x^{2} + 4 x + 1}{2 x^{2} + 3 x + 1}$

$= \frac{2 x^{3} + (3 x^{2} + 2 x^{2}) + (x + 3 x) + 1}{2 x^{2} + 2 x + 1}$

$= \frac{(2 x^{3} + 3 x^{2} + x) + (2 x^{2} + 3 x + 1)}{2 x^{2} + 3 x + 1}$

$= \frac{(2 x^{2} + 3 x + 1) (x + 1)}{2 x^{2} + 3 x + 1} = x + 1$

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