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Find all solutions using Rational Zero Theorem

Learn how to find all solutions of a polynomial equation using the Rational Zero Theorem, calculator, and synthetic division. Factor the equation if possible and solve for the remaining factors.

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Find all solutions using Rational Zero Theorem

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  1. 5.8 Rational Zero Theorem

  2. Find all solutions using rational roots: 1. Use calculator to decide which roots to test. 2. Use synthetic division to find the unknown factor (Correct if remainder = 0) 3. Repeat step 1 with this new factor until you are left with a quadratic. 4. Factor the quadratic if possible 5. Set unsolved factors to zero and solve (use the quadratic formula if you were not able to factor)

  3. 1. Find all zeros of: f(x) = x3 – 7x2 + 10x + 6

  4. Example 2: Find all zeros of the function. f(x) = x3 + 3x2 – 3x – 5

  5. 3. Find all zeros of: f(x) = 2x4 + 3x3 – 3x2 + 3x – 5

  6. 4. Find all zeros of: f(x) = x4 – 3x3 – 2x2 – 6x – 8

  7. Find all zeros of:f (x) = 2x4 + 5x3 – 18x2 – 19x + 42

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