Question

divide the polynomial x^4+3x^3-2x^2+x+10 by x+2 verify the reminder using reminder therom​

Answer 1

Step-by-step explanation:

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