Question

polynomial F(x) is divided by x and (x+1), we get remainder 0 and 1 respectively. Find the value of R(2) if R(x) is the remainder when F(x) is divided by x(x +1).

Answer 1

Hello,

R(2)=-2

Explanation:

`F(x)=q_1(x)*x+0 \ , \ F(0)=0 \\F(x)=q_2(x)*(x+1)+1\ , \ F(-1)=1\\\\F(x)=q_3*x*(x+1)+(a*x+b)\\\\if\ x=0\ then\ F(0)=0=a*0+b \Longrightarrow\ b=0\\\\if\ x=-1\ then\ F(-1)=1=a*(-1)+b \Longrightarrow\ a=-1\\\\\\R(x)=ax+b=-x\\R(2)=-2\\`