How do I factor the following trinomial?
6x^2-23x-4
(6x + 1)(x -4)
6x^2 - 23x - 4.
A*C = 6*(-4) = -24 = 1*(-24). sum = -23 = B.
6x^2 + x-24x - 4.
x(6x+1) -4(6x+1),
(6x+1)(x-4).
To factor a trinomial, follow these steps:
Step 1: Multiply the coefficient of the x^2 term by the constant term. In this case, that would be 6*(-4) = -24.
Step 2: Find two numbers that multiply to give you the value obtained in Step 1 (-24) and add up to the coefficient of the x term (-23). In this case, the numbers are -24 and 1, since -24 + 1 = -23.
Step 3: Rewrite the original trinomial by splitting the middle term (-23x) using the two numbers found in step 2. We get:
6x^2 - 24x + x - 4
Step 4: Group the terms:
(6x^2 - 24x) + (x - 4)
Step 5: Factor out the greatest common factor (GCF) from each group. In the first group, we can factor out 6x, and in the second group, we can factor out 1. We get:
6x(x - 4) + 1(x - 4)
Step 6: Notice that we now have a common binomial factor (x - 4). Factor it out:
(x - 4)(6x + 1)
So, the factored form of the trinomial 6x^2 - 23x - 4 is (x - 4)(6x + 1).