When x31-31 is divided by x-1- the remainder isa 0b 1c 30d 31

(c) 30 Let: px=x31+31 x+1=0 #8658;x= 1 By the remainder theorem, we know that when nbsp;p(x) is divided by (x + 1), the remainder is nbsp;p( 1). Thus, we ...

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Byju's Answer

Standard IX

Mathematics

Remainder Theorem

When x31=31 i...

Question

When (x³¹ = 31) is divided by (x + 1), the remainder is
(a) 0
(b) 1
(c) 30
(d) 31

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Solution

(c) 30

Let:
$p (x) = (x^{31} + 31)$
$x + 1 = 0 \Rightarrow x = - 1$
By the remainder theorem, we know that when p(x) is divided by (x + 1), the remainder is p( $-$ 1).
Thus, we have:
$p (- 1) = {(- 1)}^{31} + 31 = - 1 + 31 = 30$

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Similar questions

Q. The remainder when

x^{31} + 31

is divided by

x + 1

is :

Q. If ( x³¹ + 31) is divided by (x + 1) then find the remainder.

Q. If

x^{31} + 31

is divided by

b y x + 1

, then what will be the remainder?

Q. If x⁵¹ + 51 is divided by x + 1, the remainder is

(a) 0

(b) 1

(c) 49

(d) 50

When $p (x) = x^{4} + 2 x^{3} - 3 x^{2} + x - 1$ is divided by (x-2), the remainder is
(a) 0
(b) -1
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When (x31 = 31) is divided by (x + 1), the remainder is (a) 0 (b) 1 (c) 30 (d) 31

(c) 30 Let: px=x31+31 x+1=0⇒x=-1 By the remainder theorem, we know that when p(x) is divided by (x + 1), the remainder is p(-1). Thus, we have: p-1=-131+31 =-1+31 =30

When (x³¹ = 31) is divided by (x + 1), the remainder is
(a) 0
(b) 1
(c) 30
(d) 31

(c) 30

Let:
$p (x) = (x^{31} + 31)$
$x + 1 = 0 \Rightarrow x = - 1$
By the remainder theorem, we know that when p(x) is divided by (x + 1), the remainder is p( $-$ 1).
Thus, we have:
$p (- 1) = {(- 1)}^{31} + 31 = - 1 + 31 = 30$