Factorize completely: (h -k - p(h+k)

Question 1: Factorize completely (h^2 - k^2) - p(h+k). Step 1: Factor the difference of squares h^2 - k^2. h^2 - k^2 = (h-k)(h+k) Step 2: Substitute this into the original expression. (h-k)(h+k) - p(h+k) Step 3: Factor out the common term (h+k). (h+k)((h-k) - p) (h+k)(h-k-p) The correct option is B. The final answer is B. (h+k)(h-k-p). Question 2: A pilot flies from Lisbon to Kuala Lumpur on a bearing of 163^. If the pilot flew from Kuala Lumpur to Lisbon on the same route, find the bearing. Step 1: Identify the given bearing. The bearing from Lisbon to Kuala Lumpur is 163^. Step 2: Calculate the back bearing. To find the back bearing (from Kuala Lumpur to Lisbon), we add 180^ if the original bearing is less than 180^, or subtract 180^ if it's greater than 180^. Since 163^ < 180^, we add 180^. Back bearing = 163^ + 180^ = 343^ The correct option is D. The final answer is D. 343^. Question 3: Given that (x-2) is a factor of 8 - 2qx - x^2, find the value of q. Step 1: Apply the Factor Theorem. If (x-2) is a factor of the polynomial P(x) = 8 - 2qx - x^2, then P(2) must be equal to 0. Step 2: Substitute x=2 into the polynomial. P(2) = 8 - 2q(2) - (2)^2 P(2) = 8 - 4q - 4 P(2) = 4 - 4q Step 3: Set P(2) = 0 and solve for q. 4 - 4q = 0 4 = 4q q = (4)/(4) q = 1 The correct option is B. The final answer is B. 1. Question 4: Given that x : (3)/(4) = (1)/(2) : (9)/(8), find the value of x. Step 1: Write the proportion as an equation of fractions. (x)/(3)4 = (1)/(2)(9)/(8) Step 2: Simplify both sides of the equation. For the left side: (x)/(3)4 = x × (4)/(3) = (4x)/(3) For the right side: (1)/(2)(9)/(8) = (1)/(2) × (8)/(9) = (8)/(18) = (4)/(9) Step 3: Set the simplified expressions equal to each other. (4x)/(3) = (4)/(9) Step 4: Solve for x. Multiply both sides by 3: 4x = (4)/(9) × 3 4x = (12)/(9) 4x = (4)/(3) Divide both sides by 4: x = (4)/(3) × (1)/(4) x = (1)/(3) The correct option is B. The final answer is B. (1)/(3). Drop the next question! 📸