Polynomial Expressions and Operations
Lessons in this chapter
About Polynomial Expressions and Operations
Polynomial Expressions and Operations covers every core operation on polynomials, from basic arithmetic through factoring.
Adding, Subtracting, and Multiplying Polynomials covers the three basic operations, combining like terms and distributing across every term.
Dividing Polynomials extends division to polynomials, including long division and synthetic division for dividing by a linear factor.
Factoring Polynomials closes the chapter by reversing multiplication, breaking a polynomial back down into its factors.
The three lessons here, Adding, Subtracting, and Multiplying Polynomials, Dividing Polynomials, and Factoring Polynomials, each open as a worksheet worked in the page. Problems are scored as they are answered, so the usual slip of a dropped term partway through a long division is caught at once. All three are free to practice online.
Frequently asked questions
Adding, Subtracting, and Multiplying Polynomials treats polynomials as objects that can be combined much like numbers, with care over like terms. Dividing Polynomials covers long division and synthetic division, including what the remainder tells you about a factor, and Factoring Polynomials works in the other direction, breaking an expression back into factors using common factors, grouping, and the sum and difference of cubes. This sits in the Algebra (A) conceptual category of the high school Common Core.
Combine like terms (matching variable parts) to add or subtract, and distribute every term of one polynomial across every term of the other to multiply.
Long division works like numerical long division, one term at a time; synthetic division is a shortcut that works specifically when dividing by a linear factor (x - a).
Factoring reverses multiplication, rewriting a polynomial as a product of simpler polynomials: the reverse operation of the "Adding, Subtracting, and Multiplying" lesson.
Common techniques include factoring out a greatest common factor, factoring by grouping, and recognizing special patterns like a difference of squares or a perfect square trinomial.
Forgetting to distribute a negative sign across every term when subtracting one polynomial from another: only the first term gets negated by mistake.