Question

How do you divide `(2x^2 -7x+ 19) div(2x- 3)`?

Answer 1

"How do you" type questions are answered by explanation.

Explanation:

I use long division:

I am going to use the square root symbol, because I do not find a long division symbol in formatter but please read it as division:

`color(white)_color(white)_color(white)_color(white)_x - 2`
`2x - 3sqrt(2x^2 - 7x + 19)`
`color(white)_color(white)--2x^2 + 3x`
`color(white)_color(white)_color(white).color(white)_0 - 4x + 19`
`color(white)_color(white)_color(white)_color(white)_color(white)_4x - 6`
`color(white)_color(white)_color(white)_color(white)_color(white)_0 + 13`

The quotient is `x - 2` with remainder 13

Written as a mixed number:

`x - 2 + 13/(2x - 3)`