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
You're on a roll — here are the solutions to the factorization problems: 3.4.1 Complete the table below by identifying the common factor in each trinomial and then writing the trinomial by factoring out the common factor. | Trinomial | What is the common factor? | Write the trinomial with the Common Factor factored out. | | :-------------------- | :------------------------- | :------------------------------------------------------- | | 2x^2 + 10x + 12 | 2 | 2(x^2 + 5x + 6) | | -5a^2 - 15a - 10 | -5 | -5(a^2 + 3a + 2) | | c^3 - 8c^2 + 15c | c | c(c^2 - 8c + 15) | 3.4.2 In the table below, the mathematical steps to factorize the trinomial has been provided. Provide an explanation for each step. Factorize 3x^3 - 3x^2 - 90x. | Step | Mathematical steps | Explanation | | :--- | :----------------- | :---------- | | 1 | 3(x^3 - x^2 - 30x) | Factor out 3 which is common. | | 2 | 3x(x^2 - x - 30) | Factor out the common factor x from the terms inside the parenthesis. | | 3 | 3x(x - 6)(x + 5) | Factor the quadratic trinomial x^2 - x - 30. | What's next? Send 'em!