Dividing Polynomials

by Tanner Howell

​This is a separate example for you to view. Notice that the remainder is written a bit differently in this problem.

• Shortcut way to divide polynomials

• Uses the roots (not factor form) as the divisor

• Uses the coefficients of the terms, and not the variables, as the dividend

• 1. Change the factor form of the divisor to the root. (factor form is (x - 3), root is 3)

• 2. Write out the polynomial to be divided in descending form, writing in zeros for the terms that are missing. For example: x⁴ + 2x² + 4 would be written as: x⁴ + 0x³ + 2x² + 0x + 4

• 3. Write out the coefficients only of the polynomial, including signs and including the 0's

• 4. Write the root to the left of the coefficients with a vertical bar between it and the coefficients and a horizontal line underneath the coefficients (like an upside-down division symbol)

• 5. Bring the first coefficient down below the line, without doing anything to it

• 6. Multiply the coefficient by the root, and add the number to the next term.

• 7. Multiply the sum by the coefficient and add to the next term.