Polynomial arithmetic is a fundamental aspect of algebra involving operations such as addition, subtraction, multiplication, and division. This overview covers methods like combining like terms, the distributive property, long and synthetic division, and the application of the Zero Product Principle and Factor Theorem. These techniques are crucial for simplifying expressions and solving polynomial equations, providing students with the tools needed for mastery in mathematics.
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Polynomials are algebraic expressions composed of terms that include variables raised to non-negative integer exponents and corresponding coefficients
Addition and Subtraction
Addition and subtraction of polynomials are performed by combining like terms, which are terms with the same variable raised to the same power
Multiplication
Multiplication of polynomials can be executed using the distributive property, either horizontally or vertically
Division
Division of polynomials can be accomplished through long division or synthetic division
Factoring polynomials involves expressing a polynomial as a product of its factors, which can be monomials, binomials, or other polynomials
Addition and subtraction of polynomials are performed by combining like terms using either the horizontal or vertical method
Multiplication of polynomials can be executed using the distributive property, either horizontally or vertically
Division of polynomials can be accomplished through long division or synthetic division
Factoring is a key skill for simplifying expressions and solving equations, and can be done using techniques such as finding common factors, applying the difference of squares, and using the quadratic formula
The horizontal and vertical methods are effective for addition, subtraction, and multiplication of polynomials
Coefficients must be carefully handled when performing polynomial operations to ensure accurate results
When performing polynomial operations, missing terms must be accounted for to avoid errors
The Factor Theorem is a powerful tool for quickly identifying factors of polynomials, particularly for higher-degree polynomials
00
______ are expressions with variables to non-negative integer ______ and their coefficients.
Polynomials
exponents
01
Combining like terms in polynomials
Like terms have same variable and exponent. Combine by adding or subtracting coefficients.
02
Horizontal method for polynomial operations
Write polynomials side by side, combine like terms across expressions.
