Question

How do you divide `(x^4+2x^3+ 15 x^2+6x+8)/(x-4)`?

Answer 1

`(x^4+2x^3+15x^2+6x+8)/(x-4)=color(red)(x^3+6x^2+39x+152)" Remainder: "color(blue)(616)`

Explanation:

Do this division either using "synthetic division" or "long division"

synthetic division
`{: (,,x^4,x^3,x^2,x^1,x^0," usually omitted"), (,,1,2,15,6,8," the coefficients"), (ul(+),ul(color(white)("|")),ul(0),ul(4),ul(24),ul(146),ul(608)," product of prior row 3 value and "x"'s zero"), (4,"|",1,6,39,152,616," the 4 is the value of "x" that would make the denominator "=0), (,,x^3,x^2,x^1,x^0,R," again, this is usually omitted") :}`