Question

Find the remainder when f(x) = 2x³ - x² + x + 1 is divided by 2x + 1.A. 15B.0OC.-21D. 3/2

Answer 1

Given:

A function

`f\mleft(x\mright)=2x³-x²+x+1`

Required:

Divide f(x) by 2x + 1.

Step-by-step explanation:

The dividend is

`f(x)=2x³-x²+x+1`

and the divisor is 2x+1.

`\begin{gathered} 2x+1=0 \\ x=-(1)/(2) \end{gathered}`

Find the remainder by substituting

`x=-(1)/(2)`

in f(x).

`\begin{gathered} f(x)=2(-(1)/(2))^3-(-(1)/(2))^2+(-(1)/(2))+1 \\ f(x)=2*-(1)/(8)-(1)/(4)-(1)/(2)+1 \\ f(x)=-(1)/(4)-(1)/(4)-(1)/(2)+1 \\ f(x)=-(1)/(2)-(1)/(2)+1 \\ f(x)=-1+1 \\ f(x)=0 \end{gathered}`

The remainder is 0.

Final Answer:

Option B is the correct answer.