How to Work with Polynomials
Polynomials are the workhorses of algebra: sums of power terms like 4xยณ โ x + 9. The degree โ the highest exponent โ tells you the shape of the graph and the maximum number of roots.
Arithmetic with Polynomials
Adding and subtracting is just combining like terms across both polynomials. Multiplying means distributing every term โ FOIL is simply the 2-term special case of this general rule.
Hunting for Roots
The rational root theorem narrows the search: every rational root looks like p/q where p divides the constant term and q divides the leading coefficient. Test the candidates โ any hit is a genuine root.
Found a root and want factors? Try our factoring calculator or simplify expressions with the algebra calculator.