Find the GCF of the polynomial 44x^6+8x^5

You probably mean to factor the polynomial:

44x^6+8x^5
=4x^5(11x+2)

To find the greatest common factor (GCF) of a polynomial, we need to identify the common factors in each term and then find the highest power of each variable that appears in all terms.

Let's break down the given polynomial: 44x^6 + 8x^5.

Step 1: Identify the factors of the coefficients.
The factors of 44 are 1, 2, 4, 11, 22, and 44.
The factors of 8 are 1, 2, 4, and 8.

Step 2: Identify the highest power of the variable x in each term.
In the first term, the highest power of x is x^6.
In the second term, the highest power of x is x^5.

Step 3: Find the common factors of the coefficients and the highest powers of the variables.
The common factors of the coefficients are 1 and 2.
The common highest power of x is x^5.

Step 4: Form the GCF.
The GCF of the polynomial 44x^6 + 8x^5 is 2x^5.

Therefore, the GCF of the given polynomial is 2x^5.