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Byju's Answer

Standard VIII

Mathematics

Division of a Polynomial by a Polynomial

Polynomials ...

Question

Polynomials $p (x), g (x), q (x)$ and $r (x)$ , which satisfy the division algorithm and deg $r (x) = 0$ , are

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

;

q (x) = 5; r (x) = 7

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p (x) = 2 x^{2} + x + 1; g (x) = x + 3

;

q (x) = 2 x; r (x) = 7 x

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p (x) = x^{3} + x + 5; g (x) = x^{2} + 1

;

q (x) = x; r (x) = 5

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None of these

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Solution

The correct option is B $p (x) = x^{3} + x + 5; g (x) = x^{2} + 1$ ;
$q (x) = x; r (x) = 5$ .
option (A) and (C) have deg $r (x) = 0$ ,
in this question $p (x) = q (x) g (x) + r (x)$ is satisfied in only option (C).

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

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Single choice question:
If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) $\neq$ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when

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Polynomials p(x),g(x),q(x) and r(x), which satisfy the division algorithm and deg r(x)=0, are

The correct option is B p(x)=x3+x+5;g(x)=x2+1;q(x)=x;r(x)=5.option (A) and (C) have deg r(x)=0,in this question p(x)=q(x)g(x)+r(x) is satisfied in only option (C).

Polynomials $p (x), g (x), q (x)$ and $r (x)$ , which satisfy the division algorithm and deg $r (x) = 0$ , are

The correct option is B $p (x) = x^{3} + x + 5; g (x) = x^{2} + 1$ ;
$q (x) = x; r (x) = 5$ .
option (A) and (C) have deg $r (x) = 0$ ,
in this question $p (x) = q (x) g (x) + r (x)$ is satisfied in only option (C).