Rearrange Terms: Step Title: Rearrange the TermsConcise Step Description: Rearrange the terms of the polynomial in descending order of the powers of x.Step Calculation: The given polynomial is 9x2−8x−x3. Rearrange it to −x3+9x2−8x.Step Output: Rearranged polynomial: −x3+9x2−8x
Factor Out GCF: Step Title: Factor Out the Greatest Common Factor (GCF)Concise Step Description: Factor out the greatest common factor from the rearranged polynomial.Step Calculation: The GCF of −x3, 9x2, and −8x is x. Factor out −x from each term.Step Output: Factored polynomial: −x(x2−9x+8)
Factor the Quadratic: Step Title: Factor the QuadraticConcise Step Description: Factor the quadratic expression inside the parentheses.Step Calculation: We need to find two numbers that multiply to 8 (the constant term) and add to −9 (the coefficient of the x term). The numbers are −1 and −8. So, the quadratic factors to (x−1)(x−8).Step Output: Factored quadratic: (x−1)(x−8)
Write Final Factored Form: Step Title: Write the Final Factored FormConcise Step Description: Combine the GCF factored out in step 2 with the factored quadratic from step 3.Step Calculation: The final factored form is −x(x−1)(x−8).Step Output: Final factored form: −x(x−1)(x−8)