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.
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You're on a roll — here are the solutions to Activity 3: 3.1.1 What is the value of b and c in the trinomial? Comparing x^2 + 5x + 6 to the general form x^2 + bx + c: b = 5 c = 6 3.1.2 Use the table below to determine the two integers, r and s. | Factors of 6 | Product of the two factors | Sum of the two factors | Result | | :----------- | :------------------------- | :--------------------- | :----------------------------------- | | 1 and 6 | 1 × 6 = 6 | 1 + 6 = 7 | product = 6 but sum ≠ 5 | | -1 and -6 | (-1) × (-6) = 6 | (-1) + (-6) = -7 | product = 6 but sum ≠ 5 | | 2 and 3 | 2 × 3 = 6 | 2 + 3 = 5 | product = 6 and sum = 5 | | -2 and -3 | (-2) × (-3) = 6 | (-2) + (-3) = -5 | product = 6 but sum ≠ 5 | Which two integers will correctly provide the values of b and c in the expression x^2 + 5x + 6? The two integers are 2 and 3. 3.1.3 Rewrite x^2 + 5x + 6 as an equivalent expression in the form x^2 + rx + sx + 6. Using r=2 and s=3: x^2 + 2x + 3x + 6 The equivalent expression is x^2 + 2x + 3x + 6. 3.1.4 Use the knowledge obtained from activity 2 on grouping and the distributive property to factorize the expression. Step 1: Group the terms of the rewritten expression. (x^2 + 2x) + (3x + 6) Step 2: Factor out the common factor from each group. x(x + 2) + 3(x + 2) Step 3: Factor out the common binomial factor (x + 2). (x + 2)(x + 3) The factored expression is (x + 2)(x + 3). What's next? Send 'em!