Math, asked by pihu1520, 1 year ago

find the remainder when x⁴+ x³-2x²+ x + 1 is divided by x-1​

Answers

Answered by ShubhGandhi2903
87

p(x) = x⁴+ x³-2x²+ x + 1

By Remainder Theorem :

x - 1 = 0

x = 1

p(x) = x⁴+ x³-2x²+ x + 1

p(1) = (1)⁴ + (1)³ - 2(1)² + (1) +1

p(1) = 1 + 1 - 2 + 1

p(1) = 3 - 2

p(1) = 1

Remainder = 1

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pihu1520: your answer is wrong
pihu1520: remainder will be 2
pihu1520: so, plzz check your answer
ShubhGandhi2903: how ?
ShubhGandhi2903: i got it
pihu1520: no its wrong
ShubhGandhi2903: yes you are right i will edit it.
Answered by hukam0685
7

The remainder is 2; when x⁴+ x³-2x²+ x + 1 is divided by x-1.

Given:

  • Two polynomials.
  • x⁴+ x³-2x²+ x + 1
  • x-1

To find:

  • Find the remainder when x⁴+ x³-2x²+ x + 1 is divided by x-1.

Solution:

Theorem\Concept to be used:

Remainder Theorem: When a polynomial p(x) is divided by x-a, then remainder is given by p(a); i.e. value of polynomial at x=a.

Step 1:

Find value of x from x-1.

So,

x - 1 = 0 \\

Thus,

\bf x = 1 \\

Step 2:

Put the value of x in p(x).

Let p(x) =  {x}^{4}  +  {x}^{3}  - 2 {x}^{2}  + x + 1 \\

p(1) =  {(1)}^{4}  +  {(1)}^{3}  - 2 {(1)}^{2}  + (1) + 1 \\

or

p(1) = 1 + 1 - 2 + 1 + 1

or

\bf p(1) = 2 \\

Thus,

Remainder is 2, when x⁴+ x³-2x²+ x + 1 is divided by x-1.

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