How do you use synthetic division to divide #16x^3+8x^2-40x-115# divided by #2x-5#?

1 Answer

Answer:

#(16x^3+8x^2-40x-115)/(2x-5)=8x^2+24x+40+85/(2x-5)#

Explanation:

Use the coefficient 2 of the divisor to transform first the dividend so that

#(16x^3+8x^2-40x-115)/(2x-5)=(8x^3+4x^2-20x-115/2)/(x-5/2)#

Now, use synthetic division

The degree of the terms are already arranged so,

#" "8 " " " 4 " " " -20 " " "-115/2" " " "##|underline(" " "5/2)#
#underline(" " " " " "20" " " " "60" " " " "100)#
#" "8" " " "24" " " "40" " " "85/2" " "larr#the remainder

Write the answer

#8x^2+24x+40+(85/2)/(x-5/2)#

this is equal to

#8x^2+24x+40+85/(2x-5)#

God bless you ...