6 7 Remainder and Factor Theorem Warm Up
- Slides: 18
6 -7 Remainder and Factor Theorem Warm Up 1. Divide f(a) = 4 a 2 – 3 a + 6 by a – 2 using any method. 2. Now find f(2). 3. List any similarities. Why do you think this occurs? SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
Factor Theorem 6 -7 Remainderand Factor Theorem SWBAT • use the remainder to find the remainder of dividing polynomials. § use the factor theorem to factor polynomials Holt Mc. Dougal Algebra 2 Algebra 22 Holt Mc. Dougal SWBAT use the remainder to find the remainder of dividing polynomials. SWBAT use the factor theorem to factor polynomials
6 -7 Remainder and Factor Theorem Recall that if a number is divided by any of its factors, the remainder is 0. Likewise, if a polynomial is divided by any of its factors, the remainder is 0. The Remainder Theorem states • if a polynomial is divided by (x – a) • the remainder is the value of the function at a. SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem • Find the remainder of: – f(x) = 3 x 3 – 2 x 2 + x – 11 and x – 3 – f(x) = 4 x 5 + 2 x 3 + x 2 – 1 and x + 1 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem • Factor Theorem: – If the remainder of your equation = 0 – Then x – a is a factor of the quotient – You have to use Synthetic or Long Division • f(x) = x 4 + x 3 – 17 x 2 – 20 x + 32 and x – 4 • (x – 4) (x 3 + 5 x 2 + 3 x – 8) SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem Determine whether the given binomial is a factor of the polynomial P(x). A. (x + 1); (x 2 – 3 x + 1) Find P(– 1) by synthetic substitution. P(– 1) = 5 P(– 1) ≠ 0, so (x + 1) is not a factor of P(x) B. (x + 2); (3 x 4 + 6 x 3 – 5 x – 10) Find P(– 2) by synthetic substitution. P(– 2) = 0, so (x + 2) is a factor of P(x) SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem • Show that x + 3 is a factor of f(x) = x 3 + 6 x 2 – x – 30. Then solve for x. • (x+3)(x – 2)(x + 5), so x = -3, 2, -5 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem • Try on your own. Pg 358 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem #2
6 -7 Remainder and Factor Theorem Homework: Page 359 – #10 -22 Even Bring in book tomorrow SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem Warm Up – do not share books/ipads PG 360 # 43 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
Factor Theorem 6 -7 Remainderand Factor Theorem SWBAT § use the remainder to find the remainder of dividing polynomials. § use the factor theorem to factor Holt Mc. Dougal Algebra 2 Algebra 22 Holt Mc. Dougal polynomials SWBAT use the remainder to find the remainder of dividing polynomials. SWBAT use the factor theorem to factor polynomials
6 -7 Remainder and Factor Theorem Use the graph of the polynomial. To factor the x 3 – 3 x 2 – 6 x + 8 completely. SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem PARCC Example Answer: W: x – 4 L: x + 8 H: x – 1 Try on your own: pg 359 #3 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem Real World Example (use calc) • Pg 359 #3 -5 SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem PARCC Question Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x 3 – x 2 – 6 x. The volume V is related to the area A and the height h by the equation V = A h. Rearranging for A gives A = V. h 3 – x 2 – 6 x x A(x) = Substitute. x+2 Use synthetic division. The area of the face of the rectangular prism can be represented by A(x)= x 2 – 3 x. SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem PARCC Example Write an expression for the length of a rectangle with width y – 9 and area y 2 – 14 y + 45. The area A is related to the width w and the length l by the equation A = l w. l(x) = y 2 – 14 y + 45 y– 9 Substitute. Use synthetic division. The length of the rectangle can be represented by l(x)= y – 5. SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem Did We Reach Our Objective? § Use the factor theorem. § Use the remainder theorem. SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
6 -7 Remainder and Factor Theorem HOMEWORK • Pg 360 – # 29 – 33 all SWBAT use the remainder to find the remainder of dividing polynomials. Holt Mc. Dougal Algebra 2 to factor polynomials SWBAT use the factor theorem
