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Formation of Algebraic Expressions

Find qx and...

Question

Find $q (x)$ and $r (x)$ , for the quadratic polynomial $p (x) = 11 x - 21 + 2 x^{2}$ when divided by $1 + 2 x$

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Solution

The given polynomials $11 x - 21 + 2 x^{2}$ and $1 + 2 x$ can be rewritten as $2 x^{2} + 11 x - 21$ and $2 x + 1$ respectively.

We now divide $2 x^{2} + 11 x - 21$ by $(2 x + 1)$ as shown in the above image:

From the division, we observe that the quotient is $x + 5$ and the remainder is $- 26$ .

Hence, the quotient is $x + 5$ and the remainder is $- 26$ .

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Similar questions

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	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

P (x) = {5 x}^{5} + {3 x}^{3} - 7

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

Find q(x) and r(x) by dividing p(x) by g(x)

P (x) =

12 x^{3} - 2 x^{2} + 18

Q (x) = 2 x - 12

P (x)

Q (x)

and find the remainder.

Q. On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x) be the quotient and r(x) be the remainder, than p(x) = q(x)⋅g(x) + r(x), where

(a) r(x) = 0 always
(b) deg r (x) <deg g(x) always
(c) either r(x) = 0 or deg r(x) <deg g(x)
(d) r(x) = g(x)

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

q (x) = x^{4} - 1

r (x) = x^{3} - 2 x^{2} - 5 x + 6

, find their HCF.

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