Question

Find the remainder when p(x) = x4 + x3 – 2x2 + x + 1 is divided by x – 1÷2​

Answer 1

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\text{The remainder when }x^4+x^3-2x^2+x+1\text{ is divided by x-1 is 2}The remainder when x

4

+x

3

−2x

2

+x+1 is divided by x-1 is 2

Step-by-step explanation:

Given the polynomial

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

4

+x

3

−2x

2

+x+1

we have to find the remainder when above polynomial is divided by (x-1).

By remainder theorem

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

4

+x

3

−2x

2

+x+1

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

4

+(1)

3

−2(1)

2

+1+1

P(1)=1+1-2+2P(1)=1+1−2+2

P(1)=2P(1)=2

Hence, the remainder is 2

∴ \text{The remainder when }x^4+x^3-2x^2+x+1\text{ is divided by x-1 is 2}The remainder when x

4

+x

3

−2x

2

+x+1 is divided by x-1 is 2

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