Final answer:
To solve the equation 2x² + 3x - 20 = 0 by factorization, we need to find two numbers that multiply to the product of the coefficient of x² (2) and the constant term (-20) and add up to the coefficient of x (3). These numbers are 5 and -4. So, we rewrite the equation as (2x + 5)(x - 4) = 0. Now, we set each factor equal to zero and solve for x.
Step-by-step explanation:
To solve the equation 2x² + 3x - 20 = 0 by factorization, we need to find two numbers that multiply to the product of the coefficient of x² (2) and the constant term (-20) and add up to the coefficient of x (3). These numbers are 5 and -4. So, we rewrite the equation as (2x + 5)(x - 4) = 0. Now, we set each factor equal to zero and solve for x.
Step 1: 2x + 5 = 0 and x - 4 = 0
Step 2: Solving each equation, we get x = -5/2 and x = 4.