Question

How do you use synthetic division to divide `x^4 – 8x^3 + 16x^2 – 19` by `x-5`?

Answer 1

`x^3 -3x^2 +x+5` is the quotient and remainder is 6

Explanation:

Write the coefficients in a row and divisor 5 to the left of the first element in the row, seperated by a vertical line.

Next multiply the divisor 5 by 1 and write it below -8. Add both, to get -3 . Now multiply 5 with -3 and write -15 below 16. Add both to get 1. Next multiply 5 with 1 and write 5 below 0. Add both to get 5 and then multiply 5 with 5 and write 25 below -19. Add both to get 6. The process of division is now complete, 6 is the remainder and the quotient is `x^3 -3x^2 +x+5`