This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the greatest common factor (GCF) of the terms. The given expression is 3x^3 - 27. The terms are 3x^3 and -27. The GCF of 3 and 27 is 3. Factor out 3 from both terms: 3x^3 - 27 = 3(x^3 - 9) Step 2: Check if the remaining polynomial can be factored further. The remaining polynomial is x^3 - 9. This is not a difference of squares (a^2 - b^2) because the first term is cubed, not squared. This is not a difference of cubes (a^3 - b^3) with integer bases, because 9 is not a perfect cube of an integer (2^3 = 8 and 3^3 = 27). Therefore, x^3 - 9 cannot be factored further into polynomials with integer coefficients. The expression is completely factored as: 3(x^3 - 9) Last free one today — make it count tomorrow, or type /upgrade for unlimited.