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Polynomials and Polynomial Functions

Chapter 5. Polynomials and Polynomial Functions. 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

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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. Polynomial Equations § 5.8

  4. Quadratic Equations Quadratic Equation A second-degree polynomial equation in one variable is called a quadratic equation. Standard Form of a Quadratic Equation ax2 + bx + c = 0, a ≠ 0 where a, b, and c are all real numbers.

  5. Zero-Factor Property Zero-Factor Property For all real numbers m and n, if m · n = 0, then either m = 0 or n = 0, or both m and n = 0. Example: (x + 5)(x - 3) = 0 x + 5 = 0 or x - 3 = 0 x = -5 or x = 3

  6. Use Factoring to Solve Equations To Solve an Equation by Factoring Use the addition property to remove all terms from one side of the equation. This will result in one side of the equation being equal to 0. Combine like terms in the equation and then factor. Set each factor containing a variable equal to 0, solve the equations, and find the solutions. Check the solutions in the original equation.

  7. Example Example: Solve 4x2 = 24x.

  8. Use Factoring to Solve Applications Example A large canvas tent has an entrance in the shape of a triangle. Find the base and height of the entrance if the height is to be 3 feet less than twice the base and the total area of the entrance is 27 square feet.

  9. Use Factoring to Solve Applications Continued We use the formula for the area of a triangle to solve the problem.

  10. Use Factoring to Solve Applications Continued Since the dimensions of a geometric figure cannot be negative, we can eliminate x =-9/2 as an answer. Therefore, Base = x = 6 feet, Height = 2x – 3 = 2 (6) – 3 = 9 feet

  11. Use Factoring to Find the x-Intercepts of a Quadratic Function Example Find the x-intercepts of the graph of y = x2 – 2x – 8. The x-intercepts of the graph are (4, 0) and (-2, 0).

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