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Polynomials and Polynomial Functions

Learn how to multiply polynomials effectively using the distributive property and FOIL method, including examples and special formulas like square of binomials. Enhance your polynomial equation solving skills.

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Polynomials and Polynomial Functions

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  1. Chapter 5 Polynomials and Polynomial Functions

  2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials 5.2 – Multiplication of Polynomials 5.3 – Division of Polynomials and Synthetic Division 5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping 5.5 – Factoring Trinomials 5.6 – Special Factoring Formulas 5.7-A General Review of Factoring 5.8- Polynomial Equations

  3. Multiplication of Polynomials § 5.2

  4. Multiply a Monomial by a Polynomial To multiply polynomials, you must remember that each term of one polynomial must be multiplied by each term of the other polynomial. To multiply monomials, we use the product rule for exponents. Product Rule for Exponents

  5. Multiply a Monomial by a Polynomial Example:

  6. Multiply a Monomial by a Polynomial When multiplying a monomial by a polynomial that contains more than two terms we can use the expanded form of the distributive property. Distributive Property, Expanded Form

  7. Multiply a Monomial by a Polynomial Example:

  8. Stands for the first – multiply the first terms together. F O I L F (a + b) (c + d): product ac Stands for the outer – multiply the outer terms together. O (a + b) (c + d): product ad Stands for the inner – multiply the inner terms together. I (a + b) (c + d): product bc Stands for the last – multiply the last terms together. L (a + b) (c + d): product bd The FOIL Method Consider (a + b)(c + d): The product of the two binomials is the sum of these four products: (a + b)(c + d) = ac + ad + bc + bd.

  9. L F (7x + 3)(2x + 4) I O F O I L = (7x)(2x) + (7x)(4) + (3)(2x) + (3)(4) The FOIL Method Using the FOIL method, multiply (7x + 3)(2x + 4). = 14x2 + 28x + 6x + 12 = 14x2 + 34x + 12

  10. Find the Square of a Binomial Square of Binomials (a + b)2= (a + b)(a + b) = a2 + 2ab +b2 (a–b)2= (a–b)(a–b) = a2 – 2ab +b2 To square a binomial, add the square of the first term, twice the product of the terms and the square of the second term. Example: a.) (3x + 7)2 = 9x2 + 42x + 49 b.) (4x2 – 5y)2 = 16x4 – 40x2y+ 25y2

  11. Product of the Sum and Difference The Product of the Sum and Difference of Two Terms (a + b)(a – b) = a2 – b2 This special product is also called the difference of two squares formula. Example: a.) (2x+ 3y) (2x– 3y) = 4x2– 9y2 b.) (3x + 4/5) (3x – 4/5) = 9x2– 16/25

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