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Divide

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Divide

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  1. Divide Synthetic Division: a much faster way! by x - 1 5. 1. 2. 6. 3. The answer is x + 6 with a remainder of 12. 4.

  2. You try: Use synthetic division to divide. Answer: 5x2 - 10x + 26 - 44 x + 2

  3. The Factor Theorem: • Let f(x) be a polynomial. a. If f(c) =0, then x-c is a factor of f(x). b. If x-c is a factor of f(x), then f(c) = 0. Example 4: Solve the equation 2x3 – 3x2-11x + 6 = 0 given that 3 is a zero of f(x) = 2x3 -3x2-11x + 6. Step 1: Use synthetic division and solve. 3| 2 -3 -11 6 6 9 -6 2 3 -2 0 The remainder is 0, which means that x-3 is a factor of 2x3 -3x2-11x + 6

  4. What are the factors of 2x3 -3x2-11x + 6? • Using synthetic division, we found the factors to be (x-3)(2x2+ 3x-2) =0. • Finish factoring: (x-3) (2x-1) (x+2) =0 • Find the x- intercepts. X=3, x=1/2, x=-2 • The solution set is {-2, 1/2, 3}

  5. You try: f(x)= 15x3+14x2 -3x -2=0, given that -1 is a zero of f(x), find all factors. • Answers: -1| 15 14 -3 -2 -15 1 2 15 -1 -2 0 Factors: (x+1) (15x2 –x -2)=0 (x+1) (5x-2)(3x+1)=0 x = -1, x= 2/5, x = -1/3 Solution Set {-1, -1/3, 2/5}

  6. Summary: • Explain how the synthetic division can be used to determine if x-1 is a factor of x3 -2x2 – 11x + 12.