Polynomials −𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔 My Definition: TextbookDefinition: An expression which is the sum of terms of the form axk where k is a nonnegative integer. EXAMPLE: −𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔 My Definition:

Important Parts of a Polynomial Leading Coefficient: ______________________________________ __________________________________________ Degree of a Polynomial: __________________________________ Constant: _______________________________________________

Polynomials Chapter 10.1

Polynomials TextbookDefinition: An expression which is the sum of terms of the form axk where k is a nonnegative integer. a is a coefficient x is a variable k is an exponent EXAMPLE: 5y2 EXAMPLE: −𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔 My Definition: A string of terms connected with + and – signs. All exponents must be positive & can’t be fractions.

Not Polynomials

Polynomials in STANDARD FORM largest exponent to smallest exponent A polynomial is in standard form when the terms are written from largest exponent to smallest exponent

Important Parts of a Polynomial Leading Coefficient: When the polynomial is written in standard form, this is the coefficient of the first term Degree of a Polynomial: The largest exponent of all the terms Constant: A term with no variable

Rewrite in Standard Form Rewrite in Standard Form. Identify the leading coefficient, the degree of the polynomial and constants.

Classifying Polynomials by degree & number of terms 9

Classifying Polynomials by degree & number of terms More than 3 terms doesn’t get a special name 10

Adding & Subtracting Polynomials Chapter 10.1

Adding Polynomials Write the first expression in standard form. Leave Space or Write Zero for any “missing exponents”. Write next expression beneath, aligning like terms (same variable, same exponent) Add coefficients and constants. ***Exponents stay as they are! 12

Subtracting Polynomials Write the first expression in standard form. Leave Space or Write Zero for any “missing exponents”. Write next expression beneath, aligning like terms (same variable, same exponent) Subtract the coefficients and constants. ***Exponents stay as they are! NOTE: IT HELPS TO DISTRIBUTE THE NEGATIVE In other words, change all signs of bottom polynomial 13

Multiplying Polynomials It’s just the distributive property! When you multiply polynomials, remember that EACH Term of one polynomial must be multiplied by EACH Term of the other. When multiplying variables, use the property xa ∙ xb = xa + b