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
Here are the solutions to the factorization problems: 3.3 Julie wants to factorize the following trinomial x^2 + 9x + 20, provide her with 3 easy steps to follow. Here are the steps to factorize x^2 + 9x + 20: Step 1: Find two numbers that multiply to the constant term (20) and add up to the coefficient of the middle term (9). Step 2: Rewrite the middle term (9x) using these two numbers. For example, if the numbers are p and q, rewrite 9x as px + qx. Step 3: Group the terms into two pairs and factor out the greatest common factor (GCF) from each pair. Then, factor out the common binomial. 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. | 3 done, 2 left today. You're making progress.