Factorize 2x2 + 5x + 2 and 10a2 - 12ab - 15ab2 + 18b3. Solve n2 = 2n + 8 and 2x2 - 10x - 3 = 0.

Question 1: a) Factorize the following: i. 2x^2 + 5x + 2 Step 1: Find two numbers that multiply to 2 × 2 = 4 and add to 5. These numbers are 1 and 4. Step 2: Rewrite the middle term using these numbers. 2x^2 + x + 4x + 2 Step 3: Group the terms and factor out common factors. (2x^2 + x) + (4x + 2) x(2x + 1) + 2(2x + 1) Step 4: Factor out the common binomial. (2x + 1)(x + 2) ii. 10a^2 - 12ab - 15ab^2 + 18b^3 Step 1: Group the terms. (10a^2 - 12ab) - (15ab^2 - 18b^3) Step 2: Factor out the greatest common factor from each group. 2a(5a - 6b) - 3b^2(5a - 6b) Step 3: Factor out the common binomial. (5a - 6b)(2a - 3b^2) b) Solve the following: i. n^2 = 2n + 8 using the quadratic formula. Step 1: Rewrite the equation in standard form an^2 + bn + c = 0. n^2 - 2n - 8 = 0 Here, a=1, b=-2, c=-8. Step 2: Apply the quadratic formula n = -b ± sqrt(b^2 - 4ac)2a. n = -(-2) ± sqrt((-2)^2 - 4(1)(-8))2(1) n = 2 ± sqrt(4 + 32)2 n = 2 ± sqrt(36)2 n = (2 ± 6)/(2) Step 3: Calculate the two possible values for n. n_1 = (2 + 6)/(2) = (8)/(2) = 4 n_2 = (2 - 6)/(2) = (-4)/(2) = -2 The solutions are n=4, n=-2. ii. 2x^2 - 10x - 3 = 0 using the completing the square method. Step 1: Move the constant term to the right side. 2x^2 - 10x = 3 Step 2: Divide the entire equation by the coefficient of x^2 (which is 2). x^2 - 5x = (3)/(2) Step 3: Take half of the coefficient of x (which is -5), square it (-(5)/(2))^2 = (25)/(4), and add it to both sides. x^2 - 5x + (25)/(4) = (3)/(2) + (25)/(4) Step 4: Factor the left side as a perfect square and simplify the right side. (x - (5)/(2))^2 = (6)/(4) + (25)/(4) (x - 5