Operations and equations Polynomials Operations and equations

Subtracting Polynomials Setting up foldable Adding Polynomials + Subtracting Polynomials - Multiplying Polynomials × Dividing Polynomials ÷ Is called factoring, see page R33

Adding and Subtracting Polynomials Line up like terms (collect like terms) Like terms: terms that have the same variable and exponent Add coefficients coefficient: number in front of variable 𝟒 𝒙 𝟐 +𝟑 𝒙 𝟑 +𝒙 +( 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟑𝒙) 𝟒 𝒙 𝟐 +𝟑 𝒙 𝟑 +𝒙 −( 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟑𝒙) Line up like terms (collect like terms) Subtract coefficients

Multiplying Polynomials Terms: constants, variable, product of variables and constants (monomial),separated by addition or subtraction. Box Method: The number of rows match with the number of terms in the first factor. The number of columns match with number of terms in the second factor. (𝟑𝒙+𝟐)(𝟒𝒙+𝟕) F O I L FOIL: F first terms in parentheses O terms toward outer parentheses I terms toward inner parentheses L last terms in parentheses

Defining Polynomials Polynomial Illustration Polynomials are named by their degree and number of terms. 𝟓𝒙 𝒚 𝟐 −𝟑𝒙+𝟓 𝒚 𝟑 −𝟑 Cubic polynomial Definition An expression that can have constants, variables, and exponents, but: No division by a variable Only whole number exponents It can’t have an infinite number of terms Non-example 2 𝑥 𝑥+ 𝑦 −2 5 𝑥 1 2 Polynomial

Naming Polynomials

Greatest Common Factor Difference of Two squares Setting up foldable Greatest Common Factor GCF Difference of Two squares Quadratic Trinomial A=1 A>1

GCF and difference of squares Looking for the highest number and/or the lowest exponent on the variable that divides evenly into all terms Standard Form: Listing the terms of the polynomial from greatest to least Qualifying Questions ( 𝒂 𝟐 − 𝒃 𝟐 ) Is it a binomial? Are we subtracting? Are both terms perfect squares? If yes to ALL 3 ?’s Then, Take the square root of both terms and plug into (𝒂−𝒃)(𝒂+𝒃)

Factoring Quadratic Trinomials Quadratic is in standard form The coefficient of the middle term is the SUM The last term is the PRODUCT Draw your x and find the two numbers that satisfy the conditions Write answer as a product two binomials Slide the coefficient of the leading term to the last and multiply the two #s Divide and bottoms up