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
Alright Peter_Schemer — let's do this. Factorising a quadratic expression means rewriting it as a product of two linear expressions. For a quadratic expression of the form ax^2 + bx + c, we look for two numbers that multiply to a × c and add up to b. Let's take an example: Factorise x^2 + 5x + 6. Here, a=1, b=5, and c=6. We need two numbers that multiply to a × c = 1 × 6 = 6 and add up to b=5. The numbers are 2 and 3, because 2 × 3 = 6 and 2 + 3 = 5. Step 1: Rewrite the middle term (5x) using these two numbers: x^2 + 2x + 3x + 6 Step 2: Group the terms and factor out common factors from each group: (x^2 + 2x) + (3x + 6) x(x + 2) + 3(x + 2) Step 3: Factor out the common binomial factor (x+2): (x + 2)(x + 3) So, the factorised form of x^2 + 5x + 6 is (x+2)(x+3). Send me the next one 📸