01 Key Concepts
Polynomial Terminology
A monomial has one term (5x), a binomial has two (x+3), a trinomial has three (x^2+2x+1); polynomial covers all of these and more.
Degree of a Polynomial
The highest exponent on the variable in the expression. x^3 + 2x - 5 has degree 3.
Adding and Subtracting Polynomials
Combine like terms (matching variable parts) just as with simpler expressions.
Multiplying Polynomials
Use the distributive property, multiplying every term in the first polynomial by every term in the second (FOIL is a shortcut for two binomials: First, Outer, Inner, Last).
Standard Form
Writing a polynomial with terms in order from highest to lowest degree.
02 Key Formulas
- FOIL for (a+b)(c+d): a*c + a*d + b*c + b*d
03 Solved Examples
Example 1 Add (3x^2 + 2x - 1) + (x^2 - 5x + 4).
- Combine like terms: (3x^2+x^2) + (2x-5x) + (-1+4).
- 3x^2+x^2=4x^2. 2x-5x=-3x. -1+4=3.
Answer: 4x^2 - 3x + 3
Example 2 Multiply (x + 3)(x + 5) using FOIL.
- First: x*x = x^2.
- Outer: x*5 = 5x.
- Inner: 3*x = 3x.
- Last: 3*5 = 15.
- Combine: x^2 + 5x + 3x + 15 = x^2 + 8x + 15.
Answer: x^2 + 8x + 15
Example 3 Find the degree of the polynomial 4x^5 - 3x^2 + 7.
- Identify the highest exponent on x.
- The term 4x^5 has exponent 5, the highest in the expression.
Answer: Degree 5
04 Practice Questions
1Add (2x^2+3x) + (x^2-x+5).
3x^2+2x+5
2Subtract (5x^2+2x) - (2x^2+4x).
3x^2-2x
3Multiply (x+2)(x+4) using FOIL.
x^2+6x+8
4Find the degree of 3x^4 - x + 2.
4
5Multiply (x-3)(x+3).
x^2-9
📄 Polynomials — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.