Day 3: Daily Warm-up. Find the product and combine like terms. Simplify each expression (combine like terms)

A.3a Polynomials and Factoring Special Products and Factoring

A.3 Objectives A. Polynomials and Factoring 1.Understand the vocabulary of polynomials 2.Add and subtract polynomials 3.Write polynomials in standard form. 4.Multiply polynomials 5.Special Products 6.GCF 7.Factor Polynomials with 2 or 3 terms. 8.Factor Polynomials with more than 3 terms. 9.Find the GCF of any polynomial expression 1.Understand the vocabulary of polynomials 2.Add and subtract polynomials 3.Write polynomials in standard form. 4.Multiply polynomials 5.Special Products 6.GCF 7.Factor Polynomials with 2 or 3 terms. 8.Factor Polynomials with more than 3 terms. 9.Find the GCF of any polynomial expression

1. Vocabulary of Polynomials the product of a constant and a variable raised to a nonnegative integer power. coefficient of the monomial (constant value) variable degree of the monomial (power of the variable) Monomial: Polynomial: sum or difference of monomials

1. Vocabulary of Polynomials Special Polynomial Names if # terms is:Name: 2 terms Binomial 3 terms Trinomial Degree of Polynomial if Highest degree term is:Name: degree 1Linear degree 2Quadratic degree 3Cubic Like terms : contain same power of the variable.

2. Add/Subtract Polynomials Add the coefficients of like terms(same power of the variable) Examples

3. Standard Form and Degree Standard Form: polynomial written in descending order Definition Example Write the standard form for: The Degree of a polynomial: is the degree of the greatest degree term. Definition Example What is the degree of this polynomial?

4. Multiplying Polynomials Special case: only works with two binomials 2. Foil Method 1. Double Distribution Using the distributive property, we can multiply any number of terms

4. Multiplying Polynomials Examples for YOU to try…. Find the product and write in STANDARD form

5. Special Products These are products that occur often. You should know these! Study Tip Difference of Two Squares. Perfect Square Binomial.

6. GCF (Greatest Common Factor) GCF of coefficients: Largest number that divides into all coefficients. GCF of variable expressions: Find smallest exponent Example. Factor out the GCF Definition of Prime: If a polynomial does not factor into 2 or more polynomials, it is Prime. Definition of Prime: If a polynomial does not factor into 2 or more polynomials, it is Prime.

Factor completely State the domain of1. Day 4: Daily Warm-up. Simplify (no negative exponents) Simplify completely.

7. Factoring Polynomials Definition: Factoring is writing a polynomial as a product of polynomials of lower degree General Steps for Factoring: 1.Factor out GCFs 2.Is it a binomial (with no middle term) ? a) Is it a Difference of squares or sum/difference of cubes or or 3.Is it a trinomial (only 3 terms) apply factorization algorithm 4.If more than 3 terms grouping

5. More Special Products Difference of Two Cubes. Sum of Two Cubes.

A. Factoring Binomials Factor each. If it does not factor, state that it is PRIME Study Tip

B. Factoring Trinomials: Simple case, when 1. Factor out GCF, if there is one. 2. What multiplies to c and adds up to b? 3. Rewrite as: Example 0.

C. Factoring Algorithm for case when 1. Factor out GCF. 2. Multiply a and c 3. Find the factors of ac that add to b. 4. Rewrite the middle term bx as sum of the 2 factors. 5. Grouping. -Double bubble (check signs) -Factor out GCF in each group, if no GCF, write 1. Example 1.

Factoring Algorithm 1. Factor out GCF. 2. Multiply a and c 3. Find the factors of ac that add to b. 4. Rewrite the middle term bx as sum of the 2 factors. 5. Grouping. -Double bubble (check signs) -Factor out GCF in each group Example 2.

Factoring Algorithm for simple case, 1. Factor out GCF. 2. What multiplies to c and adds up to b? 3. We can skip rewrite of the middle term. (Why?) Example 3. Factor this polynomial using the “double bubble” algorithm. Do you get the same result?

Practice Time! completely factor the polynomial

7. Polynomial with 4 terms Ex. Use Grouping (double bubble)

Factoring Practice completely factor the polynomial 1. 2.

1. 8. Finding the GCF of an expression 2.

5. More Special Products Cubes of Binomials, or Perfect Cubes. You may wish to memorize these, but could also derive them.