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The author wants you to FOIL!

Alternative, less work! Combine both complex zeros with + sign. The author wants you to FOIL!. Isolate the i term. Square both sides. STOP! TOO MUCH WORK!. Multiply. Find the zeros of. . Rewrite f ( x ) in linear factored form. Zeros at x = -2.

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The author wants you to FOIL!

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  1. Alternative, less work! Combine both complex zeros with + sign. The author wants you to FOIL! Isolate the i term. Square both sides. STOP! TOO MUCH WORK!

  2. Multiply

  3. Find the zeros of . Rewrite f(x) in linear factored form. Zeros at x = -2 The next zero is a fraction between 0 and 1. The rational zero test gives us 1/3 or 2/3. Try 1/3. x = 1/3 We have two rational zeros and time to factor them out to a quadratic function.

  4. Find the zeros of . Rewrite f(x) in linear factored form. 3 5 25 45 -18 Zeros at x = -2 x = 1/3 x = + 3i -6 2 -54 18 -2 3 -1 27 -9 0 Factored form. ( x + 2 ) ( 3x – 1 ) ( x + 3i ) ( x – 3i ) 1 0 9 3 0 27 0 1/3 Solve for x.

  5. Find the zeros of . Given one of the zeros is x = 3 + 2i 1 -10 36 -46 -13 3 + 2i -25 – 8i 49 – 2i 13 3 + 2i 1 -7 + 2i 11 – 8i 3 – 2i 0 3 – 2i -12 + 8i -3 + 2i Go to MODE and turn on a + bi 3 – 2i 1 - 4 -1 0 Complete the square. These are the exact values!

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