Polynomials and Synthetic Division
A polynomial of degree n is a function of the form.
The degree of a polynomial function is the highest power of x in its expression. Constant (non-zero) polynomials, linear polynomials, quadratic and cubic polynomials are polynomials of degree 0, 1, 2, 3 and 4 respectively.
Long Division of Polynomials
Long division of polynomials is a lot like long division of real numbers. If the polynomials involved were written in fraction form, the numerator would be the dividend, and the denominator would be the divisor.
To divide polynomials using long division:
- Divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient.
- Multiply the new term by the divisor.
- Subtract this product from the dividend. This difference is the new dividend.
- Repeat these steps, using the difference as the new dividend until the first term of the divisor is of a greater degree than the new dividend.
If the remainder is zero, the divisor divided evenly into the dividend.
Learn more about polynomials and synthetic division below.
Polynomials and Synthetic Division
Practice: Divide polynomial functions using long or synthetic division in the following exercises.
Polynomials and Synthetic Division 1
Polynomials and Synthetic Division 2
Polynomials and Synthetic Division 3
Polynomials and Synthetic Division 4