Polynomials are expressions in algebra that consist of variables (also known as indeterminates) and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. They are foundational in algebra and are used in various fields of mathematics and science.
Key Characteristics of Polynomials
- A polynomial can have one or more terms. Each term is a product of a coefficient (a number) and a variable raised to an exponent.
- The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 3x^4 + 2x^2 – 1, the degree is 4.
- Polynomials can be classified based on the number of terms: monomials (one term), binomials (two terms), and trinomials (three terms), among others.
Examples of Polynomials
Example 1: 5x^3 – 2x^2 + 3x – 7 is a polynomial of degree 3 with four terms.
Example 2: x^2 – 4x + 4 is a polynomial of degree 2 (a quadratic polynomial) with three terms.
Operations with Polynomials
Polynomials can be added, subtracted, multiplied, and divided (except by zero). These operations follow the basic arithmetic properties but require careful application of the distributive property and combining like terms.
The Most Popular Topics:
- Corresponding angles
- Adjacent angles
- Congruent angles
- Complementary angles
- How to multiply fractions – multiplying fractions
- How to divide fractions – dividing fractions
- How to add fractions – adding fractions
- How to subtract fractions – subtracting fractions
- How to simplify fractions – simplifying fractions
- Midpoint, midpoint formula
- Quadratic formula
- Quadratic equation
- Median – what is the median in math?
- How to find median?
- Distributive property
- Associative property
- Commutative property
- Quotient – what is a quotient?
- Quotient rule
- System of equations
- Solving system of equations
- Linear equations
- Solving equations
- Slope
- Slope formula
- Slope calculator
- Point slope formula
- Slope intercept form
- How to find slope?
- Convert fraction to decimal
- Factors of a number
- Point slope form
- Slope equation
- Domain and range
- Domain – what is domain in math?
- How to find the domain of a function?
- How to find domain and range?
- Polynomial
- Polynomial long division
- Polynomial division – dividing polynomials
- Degree of polynomial
- Factoring polynomials – how to factor polynomials?
- Perpendicular lines
- Parabola equation
- Isosceles triangle
- Perimeter of triangle
- Scalene triangle
- Obtuse triangle
- Acute triangle
- Right triangle
- Trapezoid area formula
- What is a trapezoid?
- Isosceles trapezoid
- Rectangle
- Area of a rectangle
- Perimeter of a rectangle – how to find perimeter of a rectangle?
- Pythagorean theorem
- Vertex – how to find vertex?
- Vertex form
- Vertex formula
- How to find square root of a number?
Return to MathQuadrum.com from Polynomial home for more topics on mathematics