Polynomial Addition and Subtraction

Polynomials

• Polynomials are expressions or equations with terms that include a variable raised to a positive whole number exponent, possibly multiplied by a coefficient.

• Terms are listed in descending order of exponents, ending with a constant term (which can be considered the $x^0$ term).

Addition and Subtraction

• Combine like terms (terms with the same exponent on the variable).

• This is based on the distributive property.

• Treat terms like "apples"; e.g., $5x^3 + 4x^3$ is like 5 apples + 4 apples = 9 apples, so it's $9x^3$.

• When adding or subtracting, focus on manipulating the coefficients of like terms.

Adding Polynomial Expressions

• Write all terms in a line and combine like terms.

• Align expressions vertically by the degree of each term to add or subtract coefficients of like terms.

Subtraction of Polynomials

• Be careful with signs, especially when subtracting a negative term.

• Subtracting a negative is the same as adding a positive: $a - (-b) = a + b$.