6.4 Solving Polynomial Equations. One of the topics in this section is finding the cube or cube root of a number. A cubed number is the solution when.

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6.4 Solving Polynomial Equations

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Presentation transcript:

6.4 Solving Polynomial Equations

One of the topics in this section is finding the cube or cube root of a number. A cubed number is the solution when a number is multiplied by itself three times. A cube root “undos” the cubing operation just like a square root would.

FACTORING AND ROOTS CUBIC FACTORING a³ + b³ = (a + b)(a² - ab + b²) a³ - b³ = (a - b)(a² + ab + b²) Difference of Cubes Sum of Cubes Question: if we are solving for x, how many possible answers can we expect? 3 because it is a cubic!

CUBIC FACTORING EX- factor and solve 8x³ - 27 = 0 8x³ - 27 = (2x - 3)((2x)² + (2x)3 + 3²) (2x - 3)(4x² + 6x + 9)=0 Quadratic FormulaX= 3/2 a³ - b³ = (a - b)(a² + ab + b²)

CUBIC FACTORING EX- factor and solve x³ = 0 a³ + b³ = (a + b)(a² - ab + b²) x³ = (x + 7)(x² - 7x + 7²) (x + 7)(x² - 7x + 49)=0 Quadratic FormulaX= -7

Solve by Factoring by Using a Quadratic Form Ex: x 4 -2x 2 -8 = 0

Let’s Try One Solve x 4 +7x 2 +6 = 0