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
Here is a step-by-step guide on how to factorize the algebraic expression 3x^2 + 7x - 12x - 34 - 2x^2 + 10: Step 1: Combine like terms. Identify and group terms that have the same variable and exponent. (3x^2 - 2x^2) + (7x - 12x) + (-34 + 10) Step 2: Simplify the expression. Perform the addition and subtraction for each group of like terms. (3-2)x^2 + (7-12)x + (-34+10) 1x^2 - 5x - 24 The simplified expression is x^2 - 5x - 24. Step 3: Identify two numbers that multiply to the constant term and add to the coefficient of the middle term. For the quadratic trinomial x^2 - 5x - 24, we need two numbers that: • Multiply to -24 (the constant term). • Add up to -5 (the coefficient of the x term). Let's consider factors of -24: 1 × (-24) = -24, 1 + (-24) = -23 2 × (-12) = -24, 2 + (-12) = -10 3 × (-8) = -24, 3 + (-8) = -5 The two numbers are 3 and -8. Step 4: Write the expression in factored form. Using the two numbers found in Step 3, the trinomial x^2 - 5x - 24 can be factored as (x + first number)(x + second number). (x + 3)(x - 8) The factored form of the expression is (x+3)(x-8). 3 done, 2 left today. You're making progress.