Answer :

[tex]48x^{6}+6x^{2}-26x^{3}[/tex]
You can list the factors of each term:
[tex]48x^{6}:2*2*2*2*3*x*x*x*x*x*x\\
6x^{2}:2*3*x*x\\
26x^{3}:-1*2*13*x*x*x[/tex]
The only factors that repeat are 2, x, and x. So your GCF for the whole term is [tex] 2x^{2} [/tex].

Final answer:

The greatest common factor (GCF) of the terms of the polynomial 48x^6 + 6x^2 - 26x^3 is 2x^2.

Explanation:

To find the greatest common factor (GCF) of the terms of the polynomial 48x6 + 6x2 − 26x3, we need to look for the largest numerical value and the highest power of x that divides each term of the polynomial without leaving a remainder. Firstly, we determine the GCF of the coefficients: the GCF of 48, 6, and -26 is 2. Then, we look for the lowest power of x present in all terms, which in this case is x2. Thus, the GCF for the polynomial is 2x2.

Here is a step-by-step breakdown:

  1. Identify the GCF of the numerical coefficients: GCF(48, 6, -26) = 2.
  2. Identify the lowest power of x present in all the terms: the terms have x6, x2, and x3, so the lowest power is x2.
  3. Combine the numerical GCF with the lowest power of x to find the GCF of the entire polynomial: 2x2.

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