What is(6 {x}^(2) - 13x + 5)divided by(2x - 1)

Question

What is
`(6 {x}^(2) - 13x + 5)`divided by
`(2x - 1)`

Answer 1

1. Divide the first term of the dividend into the first term of the divisor:

`(6x^2)/(2x)=3x`

2. Multiply the result above by the divisor:

`3x(2x+1)=6x^2+3x`

3. Subtract the result above from the divident to get a new polynomial:

4. Repeat the process with the new polynomial:

`\begin{gathered} -(16x)/(2x)=-8 \\ \\ -8(2x+1)=-16x-8 \end{gathered}`Then, the result of the division is:
`(6x^2-13x+5)/(2x+1)=3x-8+(13)/(2x+1)`