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Factor completely:

9x^(2)-8x-x^(3)
Answer:

Factor completely:\newline9x28xx3 9 x^{2}-8 x-x^{3} \newlineAnswer:

Full solution

Q. Factor completely:\newline9x28xx3 9 x^{2}-8 x-x^{3} \newlineAnswer:
  1. Rearrange Terms: Step Title: Rearrange the Terms\newlineConcise Step Description: Rearrange the terms of the polynomial in descending order of the powers of xx.\newlineStep Calculation: The given polynomial is 9x28xx39x^2 - 8x - x^3. Rearrange it to x3+9x28x-x^3 + 9x^2 - 8x.\newlineStep Output: Rearranged polynomial: x3+9x28x-x^3 + 9x^2 - 8x
  2. Factor Out GCF: Step Title: Factor Out the Greatest Common Factor (GCF)\newlineConcise Step Description: Factor out the greatest common factor from the rearranged polynomial.\newlineStep Calculation: The GCF of x3-x^3, 9x29x^2, and 8x-8x is xx. Factor out x-x from each term.\newlineStep Output: Factored polynomial: x(x29x+8)-x(x^2 - 9x + 8)
  3. Factor the Quadratic: Step Title: Factor the Quadratic\newlineConcise Step Description: Factor the quadratic expression inside the parentheses.\newlineStep Calculation: We need to find two numbers that multiply to 88 (the constant term) and add to 9-9 (the coefficient of the xx term). The numbers are 1-1 and 8-8. So, the quadratic factors to (x1)(x8)(x - 1)(x - 8).\newlineStep Output: Factored quadratic: (x1)(x8)(x - 1)(x - 8)
  4. Write Final Factored Form: Step Title: Write the Final Factored Form\newlineConcise Step Description: Combine the GCF factored out in step 22 with the factored quadratic from step 33.\newlineStep Calculation: The final factored form is x(x1)(x8)-x(x - 1)(x - 8).\newlineStep Output: Final factored form: x(x1)(x8)-x(x - 1)(x - 8)