Find the GCF of the terms of the polynomial.
a^3 + 6a^2 - 11a
I think the GCF is a^2, but the answer key says a. Please explain.
well, since the last term is 11a, I don't see how a^2 could be a factor.
The only number or power of a which divides every term is just a.
To find the greatest common factor (GCF) of the terms of a polynomial, you need to determine the largest factor that the coefficients and variables have in common.
In the given polynomial "a^3 + 6a^2 - 11a", we can factor out the greatest common factor by looking at the exponents of the variables "a".
First, let's list out the factors of each term:
a^3 = a * a * a
6a^2 = 2 * 3 * a * a
-11a = -11 * a
As you correctly mentioned, the common factor among all terms is "a". However, the highest exponent of "a" that is common to all the terms is a^1 (a to the power of 1), not a^2. Therefore, the GCF of the terms of the polynomial is "a".
Alternatively, we can also express the polynomial factored out by the GCF:
a^3 + 6a^2 - 11a
= a(a^2 + 6a - 11)
So, the GCF of the terms is indeed "a", as confirmed by the answer key.