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HomeHomework HelpmathematicsPolynomial Operations

Polynomial Operations

Polynomial operations involve the addition, subtraction, multiplication, and scalar multiplication of polynomials, which are algebraic expressions consisting of variables raised to non-negative integer powers. Understanding these operations is essential for analyzing polynomial behavior and solving polynomial equations.

intermediate
2 hours
Mathematics
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Overview

Polynomial operations are fundamental in algebra, involving the manipulation of expressions that consist of variables raised to whole number powers. Understanding how to add, subtract, multiply, and divide polynomials is crucial for solving equations and modeling real-world situations. Mastery of th...

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Key Terms

Polynomial
An expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents.

Example: 3x² + 2x - 5

Degree
The highest power of the variable in a polynomial.

Example: In 4x³ + 2x² - x, the degree is 3.

Like Terms
Terms in a polynomial that have the same variable raised to the same power.

Example: 2x and 3x are like terms.

Coefficients
The numerical factor in a term of a polynomial.

Example: In 5x², 5 is the coefficient.

Distributive Property
A property that states a(b + c) = ab + ac.

Example: 2(x + 3) = 2x + 6.

FOIL Method
A technique for multiplying two binomials: First, Outside, Inside, Last.

Example: (x + 2)(x + 3) = x² + 5x + 6.

Related Topics

Factoring Polynomials
The process of breaking down a polynomial into simpler components that can be multiplied to get the original polynomial.
intermediate
Rational Functions
Functions that can be expressed as the ratio of two polynomials.
intermediate
Graphing Polynomials
Understanding how to graph polynomial functions and their characteristics.
intermediate

Key Concepts

Addition of PolynomialsSubtraction of PolynomialsMultiplication of PolynomialsDivision of Polynomials