How do you divide #(x^2+20x+5) / (x-4)#?

1 Answer
Mar 14, 2018

Answer:

Quotient #color(green)(x + 24)#, Remainder #color(red)(101/(x-4))#

Explanation:

Let’s use synthetic division to find the quotient and remainder.

#color(white)(aaa aaa aa aaa) 0 color(white)(aaa aa ) 1 color(white)(aaa a ) 24 #
# color(white)(aaa aaa aa ) ———————- #
# color(white)(aaa ) 4 color(white)(aaa ) | color(white)(aaa ) 1 color(white)(aaaa) 20 color(white)(a aaa) 5 #
# color(white)(aaa aaaa ) | color(white)(aa ) darr color(white)(aaa a ) 4 color(white)(aaaa) 96 #
# color(white)(aaa aaa a) | color(white)(aaa ) ——- ——- #
#color(white)(aaa aaa aaa aaa ) 1 color(white)(aa aa ) 24 color(white)(aaa) 101 #

Quotient #color(green)(x + 24)#, Remainder #color(red)(101/(x-4))#

Verification : #(x + 24) * (x - 4) = x^2 + 20x -94 + 101 = x^2 + 20x + 5#