find the greatest commom factor of the terms of the polynomial
48x^6 + 32X^2 - 26x^5
is the answer 2x^2?
Thank you
correct
To find the greatest common factor (GCF) of the terms of the polynomial 48x^6 + 32x^2 - 26x^5, we need to factor out the common terms.
First, let's find the common factor among the coefficients. The common factor of 48, 32, and -26 is 2.
Next, let's find the common factor among the variables. The common factor of x^6, x^2, and x^5 is x^2.
Now, we can take the common factor (2x^2) and factor it out from each term:
48x^6 + 32x^2 - 26x^5
= 2x^2(24x^4 + 16 - 13x^3)
Therefore, the greatest common factor of the terms of the polynomial 48x^6 + 32x^2 - 26x^5 is 2x^2, but it is not the entire polynomial itself.
To find the greatest common factor (GCF) of the terms in the polynomial 48x^6 + 32x^2 - 26x^5, we need to determine the highest power of x that can be factored out of each term.
Step 1: Identify the coefficients (numbers in front of x) of each term: 48, 32, and -26.
Step 2: Determine the highest common factor of these coefficients. In this case, the GCF of the coefficients is 2.
Step 3: Identify the highest power of x present in each term: x^6, x^2, and x^5.
Step 4: Determine the lowest power of x among the terms. In this case, it is x^2.
Step 5: Combine the GCF of the coefficients with the lowest power of x. The GCF is 2, and the lowest power of x is x^2.
Therefore, the greatest common factor of the terms in the polynomial is 2x^2. So, yes, your answer is correct. The GCF is indeed 2x^2.
Note: It is always a good practice to simplify the polynomial further if possible. In this case, you could divide each term by the GCF to simplify the polynomial to its simplest form.