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Dividend, Divisor, Quotient, Remainder

The quotient ...

Question

The quotient obtained in dividing (8x^4-2x^2+6x-7) by (2x+1) is (4x^3+ px^2-qx+3).The value of q-p is

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Q. If the quotient on dividing,

8 x^{4} - 2 x^{2} + 6 x - 7

2 x + 1

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

q - p

Q. If the quotient obtained on dividing

(8 x^{4} - 2 x^{2} + 6 x - 7)

(2 x + 1)

(4 x^{3} + p x^{2} - q x + 3)

p, q

and also the remainder.

Q. Find the quotient the and remainder of the following division:

(4 x^{3} - 2 x^{2} + 6 x + 7) \div (3 + 2 x)

Q. A polynomial

p (x)

g (x)

, the obtained quotient

q (x)

and the remainder

r (x)

are given in the table. Find

p (x)

Sl.	$p (x)$	$g (x)$	$q (x)$	$r (x)$
i	?	$x - 2$	$x^{2} - x + 1$	$4$
ii	?	$x + 3$	$2 x^{2} + x + 5$	$3 x + 1$
iii	?	$2 x + 1$	$x^{3} + 3 x^{2} - x + 1$	$0$
iv	?	$x - 1$	$x^{3} - x^{2} - x - 1$	$2 x - 4$
v	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

Q. Find the divisor

g (x)

, when the polynomial

p (x) = 4 x^{3} + 2 x^{2} - 10 x + 2

g (x)

and the quotient and remainder obtained are

(2 x^{2} + 4 x + 1)

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