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.
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Here are the solutions to the questions from the image. Question 50: The question is blurry, but it appears to be: "If x+2 is a factor of x^2+px-10, find p." Step 1: Apply the Factor Theorem. If (x+2) is a factor of the polynomial f(x) = x^2+px-10, then f(-2) must be equal to 0. Step 2: Substitute x = -2 into the polynomial. (-2)^2 + p(-2) - 10 = 0 4 - 2p - 10 = 0 Step 3: Solve for p. -2p - 6 = 0 -2p = 6 p = (6)/(-2) p = -3 Comparing this with the given options, p=-3 matches option B. The final answer is B. -3. --- Question 54: This question asks to simplify surd expressions. There are three parts. Part (i): Simplify $(sqrt(5)sqrt(3) - 2