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
Hey 💋💋CAROWW!!!💋💋, good to see you again. Step 1: Identify b and c for x^2 + 5x + 6. Comparing x^2 + 5x + 6 with the general form x^2 + bx + c: a) The value of b is 5. b) The value of c is 6. Step 2: Complete the table to find integers r and s such that their product is c=6 and their sum is b=5. | 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 | | 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 | The two integers that correctly provide the values of b and c are 2 and 3. Step 3: Rewrite x^2 + 5x + 6 in the form x^2 + rx + sx + c. Using r=2 and s=3: x^2 + 2x + 3x + 6 Step 4: Factorize the expression using grouping and the distributive property. x^2 + 2x + 3x + 6 Group the terms: (x^2 + 2x) + (3x + 6) Factor out common factors from each group: x(x + 2) + 3(x + 2) Factor out the common binomial (x + 2): (x + 2)(x + 3) Send me the next one 📸