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Division of a Polynomial by a Binomial

What is the q...

Question

What is the quotient of $\frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} + x - 6}$ ?

A

x + 1

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B

x + 2

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C

x + 3

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D

x + 4

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Solution

The correct option is B $x + 2$

$\begin{matrix} x + 2 x^{2} + x - 6 x^{3} + 3 x^{2} - 4 x - 12 x^{3} + x^{2} - 6 x - - + - -------------------- - 2 x^{2} + 2 x - 12 2 x^{2} + 2 x - 12 - - + - ------------- - 0 \end{matrix}$
Quotient = $x + 2$

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Similar questions

Q. What will be the quotient and remainder if

(3 x - 3 x^{2} - 12 + x^{4} + x^{3}) \div (2 + x^{2})

?

Q. For a polynomial, dividend is

x^{4} + 4 x - 2 x^{2} + x^{3} - 10

x^{2} + 3 x - 3 x^{2} + 4 x + 12

and remainder is

14

, then divisor is equal to

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. Divide and write the quotient and the remainder.

(3 x - 3 x^{2} - 12 + x^{4} + x^{3}) \div (2 + x^{2})

Q. Find the quotient

q (x)

r (x)

of the following when

f (x)

g (x)

.

f (x) = x^{3} - 3 x^{2} - x + 3

;

g (x) = x^{2} - 4 x + 3

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