Question

Find the remainder when x^4 +x^3 -2x^2 +x +1 is divided by x -1

Answer 1

Answer:

2

Step-by-step explanation:

Take P(x) =X^4+X^3-2X^2+X+1

By Remainder Theorem when divided by X-1 the remainder is P(1)

that is X-1=0 so X = 1.

P(1) = (1)^4+(1)^3-2(1)^2+1+1 = 1 + 1 - 2 + 1 + 1 = 2

Answer 2

To find the remainder when x^4 + x^3 – 2x^2+ x + 1 is divided by x – 1, we can use synthetic division.

First, we write the coefficients of the polynomial in decreasing order of exponents and place a placeholder for the divisor x – 1:

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   1   1   -2  1   1

1 |

Next, we bring down the first coefficient, which is 1:

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   1   1   -2  1   1

1 | 1

Then, we multiply 1 by the divisor x – 1, which gives us x – 1:

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   1   1   -2  1   1

1 | 1

   -

   0

Subtracting 0 from 1 gives us 1, which we bring down:

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   1   1   -2  1   1

1 | 1   1

   -

   0  ...

We continue this process until we have brought down all the coefficients:

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   1   1   -2  1   1

1 | 1   1   0  -2  3

   -

   0   1  -1   3 -2

Therefore, the remainder when x^4 + x^3 – 2x^2+ x + 1 is divided by x – 1 is 3.

Therefore, the correct option is (A) 3.