Answer :
To find the greatest common factor (GCF) of the polynomial
[tex]$$48x^6 + 28x^2 - 38x^3,$$[/tex]
we follow these steps:
1. GCF of the Coefficients:
Identify the coefficients of the terms, which are 48, 28, and -38. When considering their absolute values (i.e., 48, 28, and 38), the GCF of these numbers is calculated by finding the largest integer that divides each of them. This value is 2.
2. GCF of the Variable Part:
Each term has the variable [tex]$x$[/tex] raised to some exponent. The exponents are 6, 2, and 3. The GCF, in terms of the variable, is found by taking the smallest exponent among these. Thus, the variable part common to all terms is [tex]$x^2$[/tex].
3. Combine the Results:
Multiplying the GCF of the coefficients with the variable part gives the overall GCF of the polynomial:
[tex]$$\text{GCF} = 2x^2.$$[/tex]
Therefore, the GCF of the terms of the polynomial is
[tex]$$2x^2.$$[/tex]
[tex]$$48x^6 + 28x^2 - 38x^3,$$[/tex]
we follow these steps:
1. GCF of the Coefficients:
Identify the coefficients of the terms, which are 48, 28, and -38. When considering their absolute values (i.e., 48, 28, and 38), the GCF of these numbers is calculated by finding the largest integer that divides each of them. This value is 2.
2. GCF of the Variable Part:
Each term has the variable [tex]$x$[/tex] raised to some exponent. The exponents are 6, 2, and 3. The GCF, in terms of the variable, is found by taking the smallest exponent among these. Thus, the variable part common to all terms is [tex]$x^2$[/tex].
3. Combine the Results:
Multiplying the GCF of the coefficients with the variable part gives the overall GCF of the polynomial:
[tex]$$\text{GCF} = 2x^2.$$[/tex]
Therefore, the GCF of the terms of the polynomial is
[tex]$$2x^2.$$[/tex]
