6b^3 + 9b^2 - 12b
Which represents the polynomial in factored form?
(A) 3b^3 (2b^2 + 3b - 4)
(B) 3b (2b^2 + 9b^2 - 12b)
(C) 3b^2 (3b^2 + 6b - 9)
(D) 3b (2b^2 + 3b - 4)
To determine the polynomial in factored form, we need to factor out any common terms from the given expression.
The expression is: 6b^3 + 9b^2 - 12b
Looking at the coefficients (numbers) in our terms (6, 9, -12), we can see that 3 is the greatest common factor (GCF) of all three.
Next, let's factor out the GCF, which is 3b:
3b(2b^2 + 3b - 4)
Now we have factored out the GCF, we need to determine if the quadratic trinomial within the parentheses is factorable further.
The quadratic trinomial 2b^2 + 3b - 4 cannot be factored using simpler terms, so the polynomial in factored form is:
(A) 3b^3 (2b^2 + 3b - 4)