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Uncover the mystery of factoring complex trinomials!

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Tic-Tac-But No Toe Part 1: In the following tic tacs there are four numbers. Find the relationship that the two numbers on the right have with the two numbers on the left. 1. What did you find? 2. Did it follow the pattern every time?

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Tic-Tac-But No Toe Part 2: Use your discoveries from Part 1 to complete the following Tic Tacs Did your discovery work in every case? 4.Can you give any explanation for this?

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Finally! Factoring with a Frenzy! Arrange the expression in descending (or ascending) order. ax 2 + bx + c = 0 Be sure the leading coefficient is positive. Factor out the GCF, if necessary. Multiply the coefficients a and c and put the result in quadrant II of the Tic Tac. Put the coefficient b in quadrant III of the Tic Tac. Play the game! Just like the previous problems. (Find the relationship!)

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Once you have completed your Tic Tac– WHERES the ANSWER? Use the a coefficient as the numerator of two fractions. Use the results in quadrants I and IV as the two denominators. Reduce the fractions. The numerator is your coefficient for x in your binominal and the denominator is the constant term. EXAMPLE: If you get the fractions ½ and -3/5, your answer would be (x + 2) (3x – 5).

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EXAMPLES X 2 – X ? ? What 2 numbers complete the Tic Tac? Since a = 1, put a 1 in for the numerator in two fractions. You found 3 and -4. These are the denominators for the two fractions. Your fractions are 1/3 and –1/4 Your answer is (x + 3) (x – 4).

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EXAMPLES 3X 2 + 5X = ? 5 ? What 2 numbers complete the Tic Tac? Since a = 3, put a 3 in for the numerator in two fractions. You found 9 and -4. These are the denominators for the two fractions. Your fractions are 3/9 = 1/3 and –3/4 Your answer is (x + 3) (3x – 4). *Remember to re-write in standard form 3X 2 + 5X - 12

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EXAMPLES 2X 2 + 8X ? 4 ? What 2 numbers complete the Tic Tac? Since a = 1, put a 1 in for the numerator in two fractions. You found 8 and -4. These are the denominators for the two fractions. Your fractions are 1/8 and –1/4. Your answer is 2 (x + 8) (x – 4). *Remember that sometimes a GCF should be factored out before beginning. 2(X 2 + 4X – 32)

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EXAMPLES 1/2X 2 + 1/2X ? 1 ? What 2 numbers complete the Tic Tac? Since a = 1, put a 1 in for the numerator in two fractions. You found -3 and 4. These are the denominators for the two fractions. Your fractions are –1/3 and 1/4. Your answer is ½ (x – 3) (x + 4). *Remember that sometimes a GCF should be factored out before beginning. 1/2(X 2 + X – 12)

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