Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing $f (x) = 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$ by $g (x) = 2 x^{2} - x + 1$

quotient

5 x^{2} + 11 x - 28

and remainder

- 9 x + 25

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quotient

5 x^{2} - 11 x - 28

and remainder

- 9 x + 25

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quotient

5 x^{2} + 11 x - 28

and remainder

+ 9 x + 25

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quotient

5 x^{2} + 11 x - 28

and remainder

- 9 x - 25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is B quotient $5 x^{2} + 11 x - 28$ and remainder $- 9 x + 25$
So, quotient $q (x) = 5 x^{2} + 11 x - 28$ and remainder $r (x) = - 9 x + 25$ .
Now, dividend = Quotient $\times$ Divisor + Remainder
$= (5 x^{2} + 11 x - 28) (2 x^{2} - x + 1) + (- 9 x + 25)$
$= 10 x^{4} - 5 x^{3} + 5 x^{2} + 22 x^{3} - 11 x^{2} + 11 x - 56 x^{2} + 28 x - 28 - 9 x + 25$
$= 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$
Hence, the division algorithm is verified.

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