Question

x^4 +3x^3+3x^2+x+1 ÷ x+1​

Answer 1

Answer:

Given that:

P(x)=x

4

−3x

3

+2x

2

+x−1

WE know that if P(x) be a polynomial then there exist two polynomial Q(x)&R(x)such that:

P(x)=(x−2)Q(x)+R(x)...........(1)

Now

Rearrange given polynomial as:

x

4

−3x

3

+2x

2

+x−1=x

4

−2x

3

−x

3

+2x

2

+x−2+1

x

4

−3x

3

+2x

2

+x−1=x

3

(x−2)−x

2

(x−2)+1(x−2)+1

x

4

−3x

3

+2x

2

+x−1=(x

3

−x

2

+1)(x−2)+1

P(x)=(x

3

−x

2

+10)(x−2)+1..............(2)

Compering equation 1&2

R(x)=1

Remainderis1whenP(x)isdividedbyx−2

See answers in attachment...