Multiplication: To multiply two polynomials we use the laws of exponents in conjunction with the distributive law. $$(ax + b) * ( cx + d) =$$ $$ac x^2 + adx + bcx + bd =$$ $$ac x^2 + ( ad + bc) x + bd$$
Division: If f(x) and d(x)are polynomials, and the degree of d(x) is less than or equal to the degree of f(x), then there exist unique polynomials q(x) and r(x), such that
and the degree of r(x) is less than the degree of d(x).
In the special case where r(x) = 0, we say that d(x) divides evenly into f(x).
The expression q(x) is called the quotient, and the expression d(x) is called the divisor and the r(x) is called remainder.
Polynomials will show up in pretty much every section of algebra and it is important that you understand them.