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
I will solve question 7(b) from the image. The question asks to factorize the expression x^2 - x - 30. Step 1: Identify the coefficients. For a quadratic expression in the form ax^2 + bx + c, we have a=1, b=-1, and c=-30. Step 2: Find two numbers that multiply to ac and add to b. Here, ac = 1 × (-30) = -30. We need two numbers that multiply to -30 and add to -1. These numbers are 5 and -6. Step 3: Rewrite the middle term using these two numbers. x^2 - x - 30 = x^2 + 5x - 6x - 30 Step 4: Factor by grouping. Group the terms and factor out the common factors from each group. (x^2 + 5x) - (6x + 30) Factor x from the first group and 6 from the second group. x(x + 5) - 6(x + 5) Step 5: Factor out the common binomial. (x + 5)(x - 6) The factored form of x^2 - x - 30 is (x + 5)(x - 6). The final answer is (x + 5)(x - 6). Last free one today — make it count tomorrow, or type /upgrade for unlimited.