Write the expression in factored form using the ac method. Show your step-by-step work. 3x² + 8x - 3
To factor the expression 3x² + 8x - 3 using the AC method, we need to find two numbers whose product is equal to the product of the coefficient of the x² term and the constant term (-3 * 3 = -9) and whose sum is equal to the coefficient of the x term (8).
The two numbers that satisfy these conditions are 9 and -1 (-9 + 1 = 8, -9 * 1 = -9).
Step 1: Split the middle term:
3x² + 9x - x - 3
Step 2: Group the terms:
(3x² + 9x) - (x + 3)
Step 3: Factor by grouping:
3x(x + 3) - (x + 3)
Step 4: Factor out the common binomial (x + 3):
(x + 3)(3x - 1)
Therefore, the expression 3x² + 8x - 3 can be factored as (x + 3)(3x - 1).