Find the GCF of the terms of the polynomial 44x^5 and 16x^3

To find the greatest common factor (GCF) of the terms of the polynomial 44x⁵ and 16x³, we need to determine the GCF of the coefficients and the GCF of the variable parts separately.

Step 1: Finding the GCF of the coefficients

The coefficients are 44 and 16. We can find the GCF by listing the factors of each number:

• Factors of 44: 1, 2, 4, 11, 22, 44
• Factors of 16: 1, 2, 4, 8, 16

The common factors are 1, 2, and 4. The greatest of these is 4. Therefore, the GCF of the coefficients is 4.

Step 2: Finding the GCF of the variable parts

For the variable parts, we have x⁵ and x³. To find the GCF, we take the variable with the lowest exponent. Here, the lower exponent is 3, so the GCF of the variable parts is x³.

Step 3: Combining the GCFs

Now, we can combine the GCF of the coefficients and the GCF of the variables. Thus, the GCF of the terms 44x⁵ and 16x³ is:

GCF = 4x³