Question

How do you simplify `\frac { 4x ^ { 2} - 3} { x - 5}`?

Answer 1

`4x +20`
Remainder: `  (97)/(x-5)`

Explanation:

First, you inspect if there are any special products. If there are none, like in this case, you may opt to do synthetic division or long division.

Long division

`color(white)(xxxxxxxxxx)ul(4x+ color(white)(xxxxx) 20 color(white)(xxx)`
`color(white)(xxxxx) x-5 | 4x^2 color(white)(xxxxx) -3`
`color(white)(xxxxxxxxx) ul(-4x^2+20x color(white)(xxxxxx))`
`color(white)(xxxxxxxxxxxxxxx)20x- color(white)(xx)3`
`color(white)(xxxxxxxxxxxxxx) ul(-20x+100 color(white)(x))`
`color(white)(xxxxxxxxxxxxxxxxxxxxx) 97`

Synthetic Division

`ul(5) | color(white)(xx) 4 color(white)(xxxx) 0 color(white)(xxx) -3`
`color(white)(xxx) ul (color(white)(xxxxxx) 20 color(white)(xxx) 100 color(white)(xx))`
`color(white)(xxxxx)4 color(white)(xxxx) 20 color(white)(xxx) 97`

`<br>`
Answer:

`4x +20`

Remainder: `&nbsp; (97)/(x-5)`