Identify the constant term and the coefficient of the x term.

Here are the solutions to the questions: 3.3 Julie wants to factorize the following trinomial x^2 + 9x + 20. Step 1: Identify the constant term and the coefficient of the x term. The trinomial is x^2 + 9x + 20. The constant term is 20. The coefficient of the x term is 9. Step 2: Find two numbers that multiply to the constant term and add to the coefficient of the x term. We need two numbers that multiply to 20 and add up to 9. Let's list factors of 20: • 1 × 20 = 20, 1 + 20 = 21 • 2 × 10 = 20, 2 + 10 = 12 • 4 × 5 = 20, 4 + 5 = 9 The two numbers are 4 and 5. Step 3: Write the trinomial in factored form. Using the two numbers found, the trinomial can be factored as (x+4)(x+5). The factored form is (x+4)(x+5). 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. | 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. | That's 2 down. 3 left today — send the next one.