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Subtraction of Polynomials

Divide: x5+1...

Question

Divide:
$x^{5} + 11 x - 12$ by $x^{2} - 2 x + 3$

A

x^{3} + 2 x^{2} + x - 4

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B

x^{3} + 2 x^{3} + x + 4

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C

x^{3} + 2 x^{3} + x - 4

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D

x^{3} + x^{2} + x - 4

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Solution

The correct option is A $x^{3} + 2 x^{2} + x - 4$

We divide $x^{5} + 11 x - 12$ by $x^{2} - 2 x + 3$ as shown in the above image.

Hence, the answer is $x^{3} + 2 x^{2} + x - 4$ .

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Similar questions

Q. Match the following.

	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

Q. (x⁵ + x³ + x²

-

\div

\int (x + x^{2} + x^{3} + x^{4})

Q. Show that:
(i) x + 3 is a factor of

69 + 11 x - x^{2} + x^{3}

.

(ii) 2x – 3 is a factor of

x + 2 x^{3} - 9 x^{2} + 12

.

\frac{x^{2} - 7 x + 10}{x^{2} - 5 x - 14} \times \frac{x^{3} + 8}{x^{3} - 8} \times \frac{x^{2} + 2 x + 4}{x^{2} - 2 x + 4} \times \frac{x - 7}{x - 5} = ?

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