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#

#<br>#
Answer:

#4x +20#

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