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: Rearrange and combine like terms. First, group the terms with the same variable and exponent together. The given expression is: 3x^2 + 7x - 12x - 34 - 2x^2 + 10 Group the x^2 terms, x terms, and constant terms: (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: Find two numbers that multiply to the constant term and add to the coefficient of the x term. For the quadratic expression x^2 - 5x - 24, we need to find 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 quadratic expression x^2 - 5x - 24 can be factored as (x+p)(x+q), where p and q are the numbers found. (x+3)(x-8) The final factored form is (x+3)(x-8). Send me the next one 📸