6-4 Solving Polynomial Equations Factoring the sum or difference of two cubes.

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Presentation transcript:

6-4 Solving Polynomial Equations Factoring the sum or difference of two cubes

Factoring the sum of a cube 1. Take the cubed root of each term and put the new terms into a binomial with the terms separated by a plus sign 2. Using that binomial, create a trinomial –Square the first term for the first term of the trinomial –Square the last term for the last term of the trinomial –Multiply the two terms of the binomial to create the middle term of the trinomial 3. Separate the terms of the trinomial with a minus sign and then a plus sign Example: Factor x 3 + y 3 (x + y) ( x 2 – xy + y 2 )

Factoring the difference of a cube 1. Take the cubed root of each term and put the new terms into a binomial with the terms separated by a minus sign 2. Using that binomial, create a trinomial –Square the first term for the first term of the trinomial –Square the last term for the last term of the trinomial –Multiply the two terms of the binomial to create the middle term of the trinomial 3. Separate the terms of the trinomial with a two plus signs Example: Factor x 3 - y 3 (x - y) ( x 2 + xy + y 2 )

x (_____ + _____) (_____ - _____ + _____) (x + 2) (x 2 – 2x + 4) Remember: When you multiply the term of the binomial you are multiplying their absolute values – don’t get caught up on the signs – the signs of the trinomial are the same for every factorization problem of the sum of cubes you will not be able to factor the trinomial of the factored cubic binomial if you factor it correctly

8x Find the cubed root of the coefficient and the cubed root of the variable when you factor the binomial (_____ + _____) (_____ - _____ + _____) (2x + 5) (4x 2 – 10x + 25)

64x 3 – 216 Remember: this is a subtraction problem so the binomial needs to have a subtraction sign and the trinomial must have two “plus” signs (_____ - _____) (_____ + _____ + _____) (4x - 6) (16x x + 36)

64x 3 - 8y 3 Remember to find the cubed root of all of the coefficients as well as the cubed root of the variables (_____ - _____) (_____ + _____ + _____) (4x – 2y) (16x 2 + 8xy + 4y 2 )