Factor each polynomial by factoring out the GCF.
2a^2 - 4ab^2 -ab
By inspection, you will find a the GCF. The coefficient of the third term is -1, and the first term does not contain b, so numbers and b are not part of the GCF.
Divide each term by the GCF to get the factors:
2a² - 4ab² -ab
= a(2a-4b² -b)
To factor out the greatest common factor (GCF) of a polynomial, we need to find the largest term that each term in the polynomial has in common. In this case, the terms in the polynomial are 2a^2, -4ab^2, and -ab.
The first step is to identify the common factors of each term.
For 2a^2, the factors are 2, a, and a.
For -4ab^2, the factors are 2, a, b, and b.
For -ab, the factors are a and b.
Now, let's find the greatest common factor (GCF) among all the terms. We look for the term that appears in each of the factors we found above.
The GCF among all the terms is 1 a (or a), since it appears in each term.
To factor out the GCF from each term, divide each term by the GCF:
2a^2 / a = 2a
-4ab^2 / a = -4b^2
-ab / a = -b
Now, we can write the factored form of the polynomial by factoring out the GCF:
2a^2 - 4ab^2 - ab = a(2a) - b(4b^2) - b
Therefore, the factored form of the polynomial 2a^2 - 4ab^2 - ab by factoring out the GCF is:
a(2a - 4b^2 - 1b)