Answer:
To factor the quadratic expression 3x^2 - x - 4, you can use the following steps:
Check for the greatest common factor (GCF) of the coefficients. In this case, there's no common factor other than 1.
Look for two numbers that multiply to the leading coefficient (3) times the constant term (-4) and add up to the coefficient of the middle term (-1). In this case, the numbers are -4 and 3 because -4 * 3 = -12, and -4 + 3 = -1.
Rewrite the middle term (-x) using these two numbers. This is known as the "ac method."
3x^2 - 4x + 3x - 4
Group the terms and factor by grouping:
(3x^2 - 4x) + (3x - 4)
Factor out the common factor from each group:
x(3x - 4) + 1(3x - 4)
Notice that you now have a common binomial factor of (3x - 4):
(3x - 4)(x + 1)
So, the factored form of 3x^2 - x - 4 is (3x - 4)(x + 1).
Explanation: