If we divide $(10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)$ by $(2 x^{2} + 7 x - 1)$ , then the quotient is __________.

6 x^{3} + 21 x^{2} - 3 x + 5

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5 x^{2} - 9 x + 3

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5 x^{2} - 3 x + 9

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5 x^{3} - 2 x^{2} + 9 x - 3

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Solution

The correct option is B $5 x^{2} - 9 x + 3$
Let $(10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)$ be $f (x)$ and $(2 x^{2} + 7 x - 1)$ be $g (x)$ .

$f (x) = g (x) \times q (x) + r (x)$ where $q (x)$ is quotient and $r (x)$ is the remainder.

$2 x^{2} + 7 x - 1) 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3 (5 x^{2} - 9 x + 3$
$(-) 10 x^{4} + 35 x^{3} - 5 x^{2}$
$- 18 x^{3} - 57 x^{2} + 30 x$
$(-) - 18 x^{3} - 63 x^{2} + 9 x$
$6 x^{2} + 21 x - 3$
$(-) 6 x^{2} + 21 x - 3$
$0$

Therefore, quotient is $5 x^{2} - 9 x + 3$ .

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Similar questions

10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

2 x^{2} + 7 x - 1

$2 x^{2} + 7 x - 1$ completely divides $10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$ .

(5 x^{2} - 9 x + 3), (10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)

f (x) = 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

g (x) = 2 x^{2} - x + 1

x

\sqrt{{5 x}^{2} - 8 x + 3} - \sqrt{{5 x}^{2} - 9 x + 4} = \sqrt{({2 x}^{2} - 2 x)} - \sqrt{({2 x}^{2} - 3 x + 1)}

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