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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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slide2

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

slide3

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

slide4

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

slide5

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)

slide6

Ex. Factor 49x2 – 9

Step 1: Take the square root of both

(7x + 3)

(7x – 3)

slide7

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.

slide8

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)

slide9

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)