1. New Factoring: Cubics and higher

2. To factor a cubic, we have to memorize an algorithm. Ex. Factor 27x 3 - 8 Step 1: Take the cube root of the two terms (3x – 2) Step 2: Square the first and last terms. (3x – 2)(9x 2 + 4) Step 3: Multiply the two terms together and change their sign. (3x – 2)(9x 2 + 4)+ 6x

3. Ex. Factor 125x 3 + 1 Step 1: Take the cube root of the two terms (5x + 1) Step 2: Square the first and last terms. (5x + 1)(25x 2 + 1) Step 3: Multiply the two terms together and change their sign. (5x + 1)(25x 2 + 1)- 5x

4. Ex. Factor 343x 3 + 8 Step 1: Take the cube root of the two terms (7x + 1) Step 2: Square the first and last terms. (5x + 1)(25x 2 + 1) Step 3: Multiply the two terms together and change their sign. (7x + 2)(49x 2 + 4)- 14x

5. Ex. Factor 27x 5 – 8x 2 Step 1: Check for GCFs x 2 (27x 3 – 8) Step 3: Square the first and last terms. (3x – 2)(9x 2 + 4) Step 4: Multiply the two terms together and change their sign. x 2 (3x – 2) (9x 2 + 4) + 6x Step 2: Take the cube root of the two terms. (3x – 2)

6. Ex. Factor 49x 2 – 9 Step 1: Take the square root of both (7x – 3) (7x + 3)

7. Ex. Factor 49x 4 – 9 Step 1: Take the square root of both (7x 2 – 3) (7x 2 + 3) Step 2: Check to see if you can factor further.

8. Ex. Factor 16x 4 – 1 Step 1: Take the square root of both (4x 2 – 1) (4x 2 + 1) Step 2: Check to see if you can factor further. ***The first factor factors more……. (4x 2 – 1) (4x 2 + 1) (2x – 1) (2x + 1) (4x 2 + 1)

9. Ex. Factor x 4 – x 2 - 12 Step 1: If the exponents are half of each other then we can use our old methods of factoring. (x 2 + 3) (x 2 - 4) Step 2: Check to see if you can factor further. (x – 2) (x + 2) Ex. Factor x 6 – x 4 - 12 Ex. Factor x 10 – x 6 - 12 Ex. Factor x 2 – x 1 - 12 (x 2 + 3)