Answer:
To factor the quadratic function g(x) = 8x^2 - 2x - 3, we can use the following steps:
Step 1: Multiply the coefficient of the x^2 term (8) and the constant term (-3).
8 * -3 = -24
Step 2: Find two numbers that multiply to give the result from step 1 (-24) and add up to the coefficient of the x term (-2).
The two numbers that meet these criteria are -6 and +4, since -6 * 4 = -24 and -6 + 4 = -2.
Step 3: Rewrite the middle term (-2x) using the two numbers found in step 2 (-6 and +4).
8x^2 - 6x + 4x - 3
Step 4: Group the terms and factor by grouping.
2x(4x - 3) + 1(4x - 3)
Step 5: Factor out the common binomial (4x - 3).
(4x - 3)(2x + 1)
So, the factored form of the quadratic function g(x) = 8x^2 - 2x - 3 is (4x - 3)(2x + 1).