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
To factorise the quadratic expression x^2 + 5x + 6, we need to find two numbers that multiply to the constant term (6) and add up to the coefficient of the middle term (5). Step 1: Identify the coefficients. The expression is in the form ax^2 + bx + c, where a=1, b=5, and c=6. Step 2: Find two numbers that multiply to c and add to b. We are looking for two numbers, let's call them p and q, such that: p × q = 6 p + q = 5 Step 3: List pairs of factors for 6 and check their sums. • Factors of 6: (1, 6), (-1, -6), (2, 3), (-2, -3). • Sums of factors: 1 + 6 = 7 (not 5) -1 + (-6) = -7 (not 5) 2 + 3 = 5 (This is the correct sum) -2 + (-3) = -5 (not 5) Step 4: Use the identified numbers to write the factored form. The two numbers are 2 and 3. So, the factored form of the expression is (x+2)(x+3). Step 5: Compare with the given options. A. (x+1)(x+6) B. (x+2)(x+3) C. (x+1)(x+5) D. (x+3)(x+2) Both options B and D are equivalent to (x+2)(x+3) due to the commutative property of multiplication. We will select option B. The final answer is B. (x+2)(x+3). Drop the next question.