Factoring By Grouping By Brian Chamberlain Brian Fagan

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

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

Factoring When Factoring a number you break it apart into smaller numbers that can

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

Factoring By Grouping Group terms with common factors before factoring

Example 1 x 2 + 5 x + 6 Step 1: Multiply the coefficient

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

Example 1 (continued) Step 4: Group first two terms together and group the last

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

Example 2: 2 x 2 + 9 x + 10 Step 1: Multiply the

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

Example 2 (continued) Step 4: Group first two terms together and group the last

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

Example 3 x 2 – 2 x – 35 Step 1: Multiply the coefficient

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

Example 3 (continued) Step 4: Group first two terms together and group the last

Example 3 (continued) Step 4: Group first two terms together and group the last two terms together (x 2 - 7 x) + (5 x -35) Step 5: Factor 1 x( x – 7) + 5(x – 7) Step 6: Factor again (x + 5)(x - 7)

Example 4: 8 x 2 - 10 x -3 Step 1: Multiply the coefficient

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

Example 4 (continued) Step 4: Group first two terms together and group the last

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