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Byju's Answer

Standard VI

Mathematics

Formation of Algebraic Expressions

Divide the po...

Question

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder.
$p (x) = x^{3} - 3 x^{2} + 5 x - 3$
$g (x) = x^{2} - 2$

q (x) = x - 3, r (x) = 7 x + 9

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q (x) = x + 3, r (x) = - 7 x - 9

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q (x) = x + 3, r (x) = 7 x - 9

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q (x) = x - 3, r (x) = 7 x - 9

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Solution

The correct option is C $q (x) = x - 3, r (x) = 7 x - 9$
$p (x) = x^{3} - 3 x^{2} + 5 x - 3 = x^{3} - 3 x^{2} - 2 x + 6 + 7 x - 9$
$\Rightarrow p (x) = (x - 3) (x^{2} - 2) + (7 x - 9)$
$g (x) = x^{2} - 2$

Dividing $p (x)$ by $g (x)$ , we get
Quotient $q (x) = (x - 3)$ and Remainder, $R (x) = (7 x - 9)$

Hence, option D.

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Similar questions

Q. Find the value of t, given that

p (x) = x^{3} - t x^{2} + 5 x - 3,

g (x) = x^{2} - 2,

q (x) = x - 3,

r (x) = 7 x - 9

Where,

p (x)

is the dividend,

g (x)

is the divisor,

q (x)

is the quotient, and

r (x)

is the remainder

p (x) = x^{3} + 8 x^{2} - 7 x + 12

and

g (x) = x - 1

. If

p (x)

is divided by

g (x)

, it gives

q (x)

and

r (x)

as quotient and remainder respectively. If

a

is the degree of

q (x)

and

b

is the degree of

r (x)

(a - b) = ?

Q. A polynomial

p (x)

is divided by

g (x)

, the obtained quotient

q (x)

and the remainder

r (x)

are given in the table. Find

p (x)

in each case.

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

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where

(a) r(x) = 0 always

(b) deg r(x) < deg g(x) always

(d) r(x) = g(x)

$p (x) = x^{3} + 8 x^{2} - 7 x + 12$ and $g (x) = x - 1$ . If $p (x)$ is divided by $g (x)$ , it gives $q (x)$ and $r (x)$ as quotient and remainder respectively. If $a$ is the degree of $q (x)$ and $b$ is the degree of $r (x)$ , then, $(a - b) = ?$ .

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder. p(x)=x3−3x2+5x−3g(x)=x2−2

The correct option is C q(x)=x−3,r(x)=7x−9p(x)=x3−3x2+5x−3=x3−3x2−2x+6+7x−9⇒p(x)=(x−3)(x2−2)+(7x−9)g(x)=x2−2Dividing p(x) by g(x), we getQuotient q(x)=(x−3) and Remainder, R(x)=(7x−9)Hence, option D.

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder.
$p (x) = x^{3} - 3 x^{2} + 5 x - 3$
$g (x) = x^{2} - 2$