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
Step 1: Rewrite x^2 + 5x + 6 in the form x^2 + rx + sx + c. From the previous steps, we identified that for the trinomial x^2 + 5x + 6, the two integers r and s whose product is 6 and sum is 5 are 2 and 3. Therefore, we can rewrite the middle term 5x as 2x + 3x. x^2 + 2x + 3x + 6 Step 2: Factorize the expression using associative and distributive properties. We will group the terms and factor out the common factors. x^2 + 2x + 3x + 6 Group the first two terms and the last two terms: (x^2 + 2x) + (3x + 6) Factor out the greatest common factor (HCF) from each group: x(x + 2) + 3(x + 2) Now, factor out the common binomial factor (x + 2): (x + 2)(x + 3) The factorized expression is (x + 2)(x + 3). Last free one today — make it count tomorrow, or type /upgrade for unlimited.