Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Here are the step-by-step solutions for the problems. 1. Factorize x^2 + 3x + 2 Step 1: Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3). The numbers are 1 and 2, because 1 × 2 = 2 and 1 + 2 = 3. Step 2: Write the quadratic expression in factored form using these numbers. x^2 + 3x + 2 = (x + 1)(x + 2) The factored form is (x + 1)(x + 2). 2. Solve the equation (x+1)(x+2) Assuming the equation is (x+1)(x+2) = 0, as is standard for "solve the equation" when given factors. Step 1: Set each factor equal to zero. For a product of factors to be zero, at least one of the factors must be zero. x + 1 = 0 or x + 2 = 0 Step 2: Solve each linear equation for x. x + 1 = 0 x = -1 x + 2 = 0 x = -2 The solutions are x = -1, x = -2. 3. Solve for x: 5x 2y Where x=6, y=2 This question asks to "solve for x" but then provides a specific value for x. We will first solve the inequality for x in terms of y, and then verify if the given values satisfy the inequality. Step 1: Solve the inequality for x. 5x 2y Divide both sides by 5: x (2y)/(5) Step 2: Substitute the given values x=6 and y=2 into the original inequality to verify. 5(6) 2(2) 30 4 This statement is true. The solution for x in terms of y is x (2y)/(5). The given values x=6, y=2 satisfy the inequality. 4. Solve for a by dividing the equation 5a + 25 10 by -5 Step 1: Write down the inequality. 5a + 25 10 Step 2: Divide every term in the inequality by -5. Remember to reverse the inequality sign when dividing by a negative number. (5a)/(-5) + (25)/(-5) (10)/(-5) -a - 5 -2 Step 3: Isolate the term with 'a' by adding 5 to both sides. -a -2 + 5 -a 3 Step 4: Multiply both sides by -1 to solve for 'a'. Remember to reverse the inequality sign again. (-1)(-a) (-1)(3) a -3 The solution is a -3.