Question
Find the greatest common factor of the
terms of the polynomial.
Write your answer as a constant times a
product of single variables raised to
exponents.
terms of the polynomial.
product of single variables raised to
exponents.
Ask by Ellis Goodwin. in the United States
Dec 09,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor is
.
Solution
To find the greatest common factor (GCF) of the polynomial
we will first identify the coefficients and the variable parts of each term.
-
Coefficients:
- The coefficients of the terms are:
-
from , -
from , -
from , -
from .
-
The GCF of the coefficientsis . - The coefficients of the terms are:
-
Variable Parts:
- The variable parts of the terms are:
-
, -
, -
, -
.
-
For the variable, the minimum exponent present in the terms is (since does not have ). For the variable, the exponents are . The minimum exponent is . Therefore, the GCF for the variable parts is. - The variable parts of the terms are:
-
Combining the GCFs:
Now, we combine the GCF of the coefficients and the GCF of the variable parts:
Thus, the greatest common factor of the terms of the polynomial is
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Bonus Knowledge
To find the greatest common factor (GCF) of the polynomial
, we first look at the coefficients and then at the variables.
The coefficients are
and
. The GCF of these coefficients is
.
Next, for the variable
, the smallest exponent of
present in all terms is
(since the terms have
and
).
Lastly, the variable
appears only in the first term, so it does not contribute to the GCF.
Putting it all together, the GCF of the polynomial is: