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 — 3.1.3 Rewrite x^2 + 5x + 6 as an equivalent expression in the form x^2 + rx + sx + 6. Step 1: Identify the values for r and s. From the previous activity (question 2.5, which was part of 3.1), the two integers that multiply to 6 and add to 5 are 2 and 3. So, r=2 and s=3. Step 2: Substitute r and s into the expression. 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 from the expression in 3.1.3. (x^2 + 2x) + (3x + 6) Step 2: Factor out the common factor from the first group. x(x + 2) Step 3: Factor out the common factor from the second group. 3(x + 2) Step 4: Combine the factored groups. x(x + 2) + 3(x + 2) Step 5: Factor out the common binomial factor (x + 2). (x + 2)(x + 3) The factorized expression is (x + 2)(x + 3). Drop the next question!