Solve each quadratic equation by factoring.a. x2 − 5x + 4 = 0b. 9y2 − 1 = 0c. 5x2 = 10x

a. x² - 5x + 4 = 0

Step 1: Identify the coefficients of the quadratic equation. Here, a = 1, b = -5, and c = 4.

Step 2: Factor the quadratic equation. We need to find two numbers that multiply to 4 (ac) and add to -5 (b). The numbers are -4 and -1.

Step 3: Rewrite the equation: x² - 4x - x + 4 = 0

Step 4: Factor by grouping: x(x - 4) - 1(x - 4) = 0

Step 5: Combine like terms: (x - 4)(x - 1) = 0

Step 6: Set each factor equal to zero and solve for x: x - 4 = 0 or x - 1 = 0. Solving for x gives x = 4 or x = 1.

b. 9y² - 1 = 0

Step 1: Identify the coefficients of the quadratic equation. Here, a = 9, b = 0, and c = -1.

Step 2: This is a difference of squares, which can be factored as (3y - 1)(3y + 1) = 0.

Step 3: Set each factor equal to zero and solve for y: 3y - 1 = 0 or 3y + 1 = 0. Solving for y gives y = 1/3 or y = -1/3.

c. 5x² = 10x

Step 1: Rewrite the equation in standard form: 5x² - 10x = 0

Step 2: Factor out the greatest common factor, which is 5x: 5x(x - 2) = 0

Step 3: Set each factor equal to zero and solve for x: 5x = 0 or x - 2 = 0. Solving for x gives x = 0 or x = 2.