Question

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

Answer 1

`(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 ...