Polynomial facts for kids

A polynomial is a special kind of math expression. It's made by adding or subtracting several smaller parts called terms. Each term can be a number, a variable (like 'x' or 'y'), or a number multiplied by one or more variables.

You often see polynomials in algebra. They look like a mix of numbers, letters, and math operations. For example, 7x⁴-3x³+19x²-8x+197 is a polynomial.

In algebra, letters like 'x' or 'y' are called variables. They stand for numbers that might be unknown or that can change. Polynomials only use addition, subtraction, multiplication, and whole number exponentiation (like x² or x³). If an expression uses division or square roots, it's not a polynomial.

Polynomials are very useful. Mathematicians, scientists, and engineers use them to solve many problems. They can form equations, like 7x⁴-3x³+19x²-8x+197 = 0. They can also form functions, like f(x) = 7x⁴-3x³+19x²-8x+197.

Understanding Polynomial Parts

Let's break down what makes up a polynomial. Each part of a polynomial separated by a plus or minus sign is called a "term".

For example, in the polynomial 7x⁴-3x³+19x²-8x+197, the terms are:

• 7x⁴
• -3x³
• +19x²
• -8x
• +197

When you see a number next to a letter, it means multiplication. So, 2x means 2 times x. If x is 7, then 2x is 14.

What are Coefficients, Variables, and Exponents?

In a term, each part has a special name:

• The number in front of the variable is called the coefficient. For example, in 5x³, 5 is the coefficient.
• The letter (like x) is the variable. It's the unknown value.
• The small raised number after the variable is the exponent. It tells you how many times to multiply the variable by itself. In 5x³, 3 is the exponent. On computers, you might see x^3 instead of x³.

Types of Polynomials by Terms

Polynomials get special names based on how many terms they have:

• A polynomial with only one term is a monomial. For example, 5x³ is a monomial. Monomials are the basic building blocks of all polynomials.
• A polynomial with exactly two terms is a binomial.
• A polynomial with exactly three terms is a trinomial.

Understanding Term Degrees

Terms also have a "degree," which is based on their exponent:

• A term with no variables (just a number) is a constant term. It has a degree of zero.
• A term with one variable and no exponent (like x, which means x¹) is a first degree term or linear term.
• A term with one variable that has an exponent of 2 (like x²) is a second degree term or quadratic term. A quadratic equation is an equation where the highest exponent is 2.
• A term with one variable that has an exponent of 3 (like x³) is a third degree term or cubic term. A cubic equation has a highest exponent of 3.
• A term with one variable that has an exponent of 4 (like x⁴) is a fourth degree term or quartic term. A quartic equation has a highest exponent of 4.
• A term with one variable that has an exponent of 5 (like x⁵) is a fifth degree term or quintic term. A quintic equation has a highest exponent of 5.
• A term with one variable that has an exponent of 6 (like x⁶) is a sixth degree term or sextic term. A sextic equation has a highest exponent of 6.

Related Math Topics

• Degree (mathematics)
• Fundamental theorem of algebra
• Polynomial remainder theorem
• Polynomial root

See also

In Spanish: Polinomio para niños