By, Brian Chamberlain, Brian Fagan, Catherine Perry, and Lauren Jones

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Presentation transcript:

By, Brian Chamberlain, Brian Fagan, Catherine Perry, and Lauren Jones Factoring By Grouping By, Brian Chamberlain, Brian Fagan, Catherine Perry, and Lauren Jones 2B

Factoring When Factoring a number you break it apart into smaller numbers that can multiplied together to get the original.

Factoring By Grouping Group terms with common factors before factoring

Example 1 Example 1 x2 + 5x + 6 Step 1: Multiply the coefficient of x2 and the constant 1 * 6 = 6 Step 2: Find two factors of 6 that add up to 5 2 and 3 Step 3: Replace 5x with 2x and 3x x2 + 2x + 3x + 6

Example 1 (continued) Step 4: Group first two terms together and group the last two terms together (x2 + 2x) + (3x + 6) Step 5: Factor x(x + 2) + 3(x + 2) Step 6: Factor again (x + 2) (x + 3)

Example 2 Example 2: 2x2 + 9x + 10 Step 1: Multiply the coefficient of x2 and the constant 2* 10= 20 Step 2: Find two factors of 20 that add up to 9 4 and 5 Step 3: Replace 9x with 4x and 5x 2x2 + 4x + 5x + 10

Example 2 (continued) Step 4: Group first two terms together and group the last two terms together (2x2 + 4x) + (5x + 10) Step 5: Factor 2x(x + 2) + 5(x + 2) Step 6: Factor Again (x + 2) (2x + 5)

Example 3 Example 3 x2 – 2x – 35 Step 1: Multiply the coefficient of x2 and the constant 1 * -35 = -35 Step 2:Find factors of -35 that add up to -2 -7 and 5 Step 3: Replace -2x with -7x and 5x x2 -7x + 5x - 35

Example 3 (continued) Step 4: Group first two terms together and group the last two terms together (x2 - 7x) + (5x -35) Step 5: Factor 1x( x – 7) + 5(x – 7) Step 6: Factor again (x + 5)(x - 7)

Example 4 Example 4: 8x2 - 10x -3 Step 1: Multiply the coefficient of x2 and the constant 8 * -3 = -24 Step 2: Find factors of -24 that add up to -10 12 and 2 Step 3: Replace -10x with -12x and 2x 8x2 + 2x + -12x -3

Example 4 (continued) Step 4: Group first two terms together and group the last two terms together (8x2 + 2x) + (-12x – 3) Step 5: Factor 2x(4x + 1) + -3(4x + 1) Step 6: Factor again (4x + 1) (2x – 3)