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

1 Answer
Oct 10, 2017

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

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Answer:

4x +20

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