Factor by grouping:
x to the third power +4x square-3x-12
Glen/Taegan, stop switching names.
x^3 + 4x^2 - 3x - 12.
(x^3 + 4x^2) + (-3x -12)
x^2 (x + 4) -3(x + 4)
(x + 4)(x^2 -3)
To factor by grouping, we'll need to rearrange the terms in a specific way. Let's consider the expression:
x^3 + 4x^2 - 3x - 12
Step 1: Group the terms in pairs:
(x^3 + 4x^2) - (3x + 12)
Step 2: Find the greatest common factor (GCF) for each pair.
The GCF of the first pair (x^3 and 4x^2) is x^2.
The GCF of the second pair (3x and 12) is 3.
Step 3: Factor out the GCF from each pair:
x^2(x + 4) - 3(x + 4)
Step 4: Observe that we now have a common binomial factor, (x + 4).
Step 5: Factor out the common binomial factor:
(x^2 - 3)(x + 4)
Therefore, the factored form of the expression x^3 + 4x^2 - 3x - 12 is (x^2 - 3)(x + 4).