Factor Theorems.

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Presentation transcript:

Factor Theorems

The Factor Theorem

Solve the equation 2x3-3x2-11x+6=0 given that 3 is a zero of f(x)=2x3-3x2-11x+6. The factor theorem tells us that x-3 is a factor of f(x). So we will use both synthetic division and long division to show this and to find another factor. Another factor

Example Solve the equation x3- 5x2 + 9x - 45 = 0 given that 5 is a zero of f(x)= x3- 5x2 + 9x – 45. Consider all complex number solutions.

Answer Solve the equation x3- 5x2 + 9x - 45 = 0 given that 5 is a zero of f(x)= x3- 5x2 + 9x – 45. Consider all complex number solutions.

Example Solve the equation x4- 6x2 - 8x + 24 = 0 given that 2 is a zero twice of function. Consider all complex number solutions.

Example Solve the equation x4- 6x2 - 8x + 24 = 0 given that 2 is a zero twice of function. Consider all complex number solutions.