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Chapter 7: Polynomials

Chapter 7: Polynomials. This chapter starts on page 320, with a list of key words and concepts. Chapter 7: Get Ready!. Here are the concepts that need to be reviewed before starting Chapter 7: Represent expressions using algebra tiles. The zero principle Polynomials Factors.

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Chapter 7: Polynomials

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  1. Chapter 7: Polynomials This chapter starts on page 320, with a list of key words and concepts.

  2. Chapter 7: Get Ready! • Here are the concepts that need to be reviewed before starting Chapter 7: • Represent expressions using algebra tiles. • The zero principle • Polynomials • Factors

  3. 7.1 Add and Subtract Polynomials! • A term is an expression formed by the product of numbers and variables. • 3x2 et 4x are examples of terms.

  4. What is a variable? • A variable is a letter that is used to represent a value that can change or vary. • For example, in 4x – 1, the variable is x.

  5. There are 2 parts of a term: The numerical coefficient The literal coefficient The parts of a term

  6. The numerical coefficient • The numeric factor of a term is called the numerical coefficient. • For example, the numerical coefficient of 4x is 4.

  7. The literal coefficient • The non-numeric factor (i.e. the letter) of a term is called the literal coefficient. • For example, the literal coefficient of 4x is x.

  8. A polynomial • A polynomial is an algebraic expression consisting of one or more terms separated by addition (+) or subtraction (-) symbols.

  9. There are 4 different types of polynomials: Monomials Binomials Trinomials Polynomials Types of polynomials

  10. The definition of each polynomial • A monomial has one term. • A binomial has two terms. • A trinomial has three terms. • A polynomial is an expression having 4 terms or more.

  11. Like terms • Like terms are terms that have the same literal coefficient. • For example, 3x et 4x are like terms because they have the same literal coefficient, x.

  12. An algebraic model • An algebraic model can represent a pattern, a relationship or a numeral sequence. • An algebraic model is always written in the form of an algebraic expression, algebraic equation or algebraic formula.

  13. 7.3: Multiply a monomial by a polynomial • Here is the distributive property, a rule that allows you to simplify expressions involving the multiplication of a monomial by a polynomial. • 3(x + 2) = 3(x) + 3(2) = 3x + 6

  14. The expansion of expressions • When you apply the distributive property, you are expanding an expression.

  15. In order to multiply 2 binomials, there are 2 methods we can use: Area models using Alge-Tiles. F.O.I.L. 7.4: Multiply two binomials

  16. The area of a rectangle Area of a rectangle = length of rectangle x width of rectangle

  17. Method #1 (Area models) • When building rectangular tile models, use these directions: • Begin at the bottom left corner with x2 tiles first. • Construct a rectangle in the top right corner with unit tiles. • Fill the top left and bottom right spaces with x-tiles.

  18. Method #2 (F.O.I.L.) • In order to use the F.O.I.L. method properly, use these directions: • The F: multiply the 2 first terms together • The O: multiply the 2 outer terms together • The I: multiply the 2 interior terms together • The L: multiply the 2 last terms together • Add all the products together in order to obtain the simplified expression.

  19. The result of multiplying 2 binomials • When you multiply 2 binomials together, you will get a trinomial *** • For example: • (x + 2)(x + 3) = x2 + 5x + 6

  20. 7.5: Polynomial Division • To divide a polynomial by a monomial, it is like applying the distributive property in reverse. • For example, (6x + 9) ÷ 3 = (6x/3) + (9/3) = 2x + 3 • *** A number divided by itself equals 1. (4÷4=1 et x÷x=1)

  21. There are 3 ways to factor a polynomial: The sharing model The area model The greatest common factor method 7.2: Common Factors

  22. Factoring a polynomial • In order to factor a polynomial completely, find the polynomial’s greatest common factor. • You can find these common factors in the numerical coefficients, in the literal coefficients or in the both of them.

  23. Which method should you use? • The sharing model works best when the common factor is a number. • The area model works best when the common factor is a letter.

  24. An example of factoring • 3x + 12 = 3(x + 4) • 3x + 12 = 3(x + 4) are equivalent expressions.

  25. The expanded form • 3x + 12 is in the expanded form and contains two terms.

  26. The factored form • 3(x + 4) is in the factored form. • The factored form has 2 types of factors: 3 is the common numeric factor and (x + 4) is the polynomial factor.

  27. 7.6: Applying algebraic modeling • Here is how you can solve an algebraic word problem: • Read the problem at least 3 times. • Identify the known and unknown quantities. • Make a plan that will solve for the unknown quantities. • Solve your problem with the plan that you came up with in #3. • Write your final answer in a complete sentence.

  28. The summary of Chapter 7 • What did we learn about in this chapter?

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