How do you use synthetic division to divide #(12x^4 + 20x^3 - 24x^2 + 20x + 35) # by #3x+5#?

1 Answer
Jul 11, 2018

Answer:

The remainder is #-65# and the quotient is #=4x^3-8x+20#

Explanation:

Let's perform the synthetic division

Divide by #3#

#color(white)(aaaa)##-5/3##|##color(white)(aaaa)##4##color(white)(aaaa)##20/3##color(white)(aaaaaa)##-8##color(white)(aaaaaa)##20/3##color(white)(aaaa)##35/3#

#color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##-20/3##color(white)(aaaaaa)##0##color(white)(aaaaaaa)##40/3##color(white)(aaa)##-100/3#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaaaa)##|##color(white)(aaaa)##4##color(white)(aaaaa)##0##color(white)(aaaaaaa)##-8##color(white)(aaaaaaa)##20##color(white)(aaaa)##color(red)(-65/3)#

The remainder is #-65# and the quotient is #=4x^3+0x^2-8x+20#

#(12x^4+20x^3-24x^2+20x+35)/(3x+5)=4x^3-8x+20-(65/3)/(x+5/3)#

#=4x^3-8x+20-(65)/(3x+5)#