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: Factorize the first expression. The expression is X^2 - 11X + 30. We need to find two numbers that multiply to 30 and add up to -11. These numbers are -5 and -6. X^2 - 11X + 30 = X^2 - 5X - 6X + 30 Step 2: Group the terms and factor out common factors. X(X - 5) - 6(X - 5) Step 3: Factor out the common binomial (X - 5). (X - 5)(X - 6) The factorization for part i is (X - 5)(X - 6). Step 4: Factorize the second expression. The expression is 25X^2 - 9. This is in the form of a difference of squares, a^2 - b^2 = (a - b)(a + b). Here, a^2 = 25X^2, so a = sqrt(25X^2) = 5X. And b^2 = 9, so b = sqrt(9) = 3. Step 5: Apply the difference of squares formula. 25X^2 - 9 = (5X)^2 - (3)^2 = (5X - 3)(5X + 3) The factorization for part ii is (5X - 3)(5X + 3). Drop the next question 📸