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New Factoring: Cubics and higher

New Factoring: Cubics and higher. 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. (9x 2 + 4). (3x – 2). Step 3: Multiply the two terms together and

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New Factoring: Cubics and higher

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  1. New Factoring: Cubics and higher

  2. To factor a cubic, we have to memorize an algorithm. Ex. Factor 27x3 - 8 Step 1: Take the cube root of the two terms (3x – 2) Step 2: Square the first and last terms. (9x2 + 4) (3x – 2) Step 3: Multiply the two terms together and change their sign. (3x – 2) (9x2 + 4) + 6x

  3. Ex. Factor 125x3 + 1 Step 1: Take the cube root of the two terms (5x + 1) Step 2: Square the first and last terms. (25x2 + 1) (5x + 1) Step 3: Multiply the two terms together and change their sign. (5x + 1) (25x2 + 1) - 5x

  4. Ex. Factor 343x3 + 8 Step 1: Take the cube root of the two terms (7x + 1) Step 2: Square the first and last terms. (25x2 + 1) (5x + 1) Step 3: Multiply the two terms together and change their sign. (7x + 2) (49x2 + 4) - 14x

  5. Ex. Factor 27x5 – 8x2 Step 1: Check for GCFs x2 (27x3 – 8) Step 2: Take the cube root of the two terms. (3x – 2) Step 3: Square the first and last terms. (9x2 + 4) (3x – 2) Step 4: Multiply the two terms together and change their sign. (9x2 + 4) + 6x x2 (3x – 2)

  6. Ex. Factor 49x2 – 9 Step 1: Take the square root of both (7x + 3) (7x – 3)

  7. Ex. Factor 49x4 – 9 Step 1: Take the square root of both (7x2+ 3) (7x2 – 3) Step 2: Check to see if you can factor further.

  8. Ex. Factor 16x4 – 1 Step 1: Take the square root of both (4x2 + 1) (4x2 – 1) Step 2: Check to see if you can factor further. ***The first factor factors more……. (4x2 + 1) (4x2 – 1) (2x – 1) (2x + 1) (4x2 + 1)

  9. Ex. Factor x6 – x4- 12 Ex. Factor x10 – x6 - 12 Ex. Factor x2 – x1 - 12 Ex. Factor x4 – x2 - 12 Step 1: If the exponents are half of each other then we can use our old methods of factoring. (x2 + 3) (x2 - 4) Step 2: Check to see if you can factor further. (x2 + 3) (x + 2) (x – 2)

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