Factoring Fanatic PowerPoint Math III: Unit 2, Lesson 2 Factoring Fanatic PowerPoint Adapted from Factoring Fanatic Lesson by Leah Drauch West Point Middle School Cullman, Alabama

Tic-Tac-But No Toe Part 1: In the following tic-tac’s there are four numbers. Find the relationship that the two numbers on the right have with the two numbers on the left. -90 10 1 -9 36 -6 -12 -36 -6 6 -30 -6 -1 5 -6 -3 -1 2 -49 7 -7 120 30 34 4 -81 9 -9 24 -6 -10 -4 49 -7 -14 -72 24 21 -3 16 4 8 Observations 1. What did you find? 2. Did it follow the pattern every time?

Tic-Tac-But No Toe Part 2: Use your discoveries from Part 1 to complete the following Tic-Tac’s. 9 10 16 -10 18 9 6 7 -35 2 4 -5 45 14 6 -5 -3 -2 -15 2 72 -38 -6 -5 -72 -1 -36 5 -22 9

Did your discovery work in every case? Observations Did your discovery work in every case? Do the numbers on the right always multiply and add to produce the numbers on the left? Can you give any explanation for this? How could this help us in factoring?

Finally! Factoring with a Frenzy! Arrange the expression in descending (or ascending) order. ax2 + 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!)

Once you have completed your Tic-Tac, WHERE’S 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 1/2 and -3/5, your answer would be (x + 2) (3x – 5).

EXAMPLES X2 – X – 12 -12 ? -1 What 2 numbers complete the Tic-Tac? -12 3 -1 -4 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).

EXAMPLES 3X2 + 5X = 12 *Remember to re-write in standard form 3X2 + 5X - 12 -36 ? 5 What 2 numbers complete the Tic Tac? -36 9 5 -4 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).

EXAMPLES 2X2 + 8X - 64 *Remember that sometimes a GCF should be factored out before beginning. 2(X2 + 4X – 32) -32 ? 4 What 2 numbers complete the Tic Tac? Since a = 1, put a 1 in for the numerator in two fractions. -32 8 4 -4 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).

EXAMPLES -12 ? 1 -12 -3 1 4 What 2 numbers complete the Tic Tac?     -12 ? 1 What 2 numbers complete the Tic Tac? Since a = 1, put a 1 in for the numerator in two fractions. -12 -3 1 4   It may be interesting to point out here that this is example is nearly the same as the one found on slide 7. The only differences in the problems are the sign of the linear term is different, and the coefficients are different in this example. (But once you factor out the 1/2, the sign is the only difference in the problem.) How does this subtle change affect your answer?