Question

How do you use synthetic division to divide `6n^4-33n^3+16n^2+5n-55` by `n-5`?

Answer 1

Quotient is `6n^3-3n^2+n+10` and Remainder is -5

Explanation:

First write all the coefficients of n^4, n^3. n^2, n, and the constant term in a row. Since divisor is n-5, write 5 on the left of the left most digit in the row, seperated by a vertical line. Now, first multiply 5 with 6 and write 30 below -33. Add both of them and write -3 ,down below.
Next multiply 5 with -3 and write -15 below 16. Add both of them and write 1 down ,below.

Next multiply 5 with 1 and write 5 below 5. Add both of them and write 10, down below.

Next multiply 5 with 10 and write 50 below -55. Add both of them and write -5, down below.

That is the end of process. -5 is the remainder and the coefficients of the quotient will be 6, -3,1 and 10

Quotient is `6n^3 -3n^2 +n +10`. Remainder is -5