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 factorize the expression x^2(2a+3b) + 3x(2a+3b) + 2(2a+3b), we can identify the common factor. Step 1: Identify the common binomial factor. The term (2a+3b) is common to all three parts of the expression. Step 2: Factor out the common term. Factor out (2a+3b) from the entire expression: (2a+3b)(x^2 + 3x + 2) Step 3: Factorize the quadratic expression inside the parentheses. We need to factorize x^2 + 3x + 2. We look for two numbers that multiply to 2 and add up to 3. These numbers are 1 and 2. So, x^2 + 3x + 2 can be factored as (x+1)(x+2). Step 4: Combine all factors. Substitute the factored quadratic back into the expression: (2a+3b)(x+1)(x+2) The factored expression is: (2a+3b)(x+1)(x+2) 3 done, 2 left today. You're making progress.