factor the expression below using the greatest common facror
12n^5 + 8n^3 +6n
To factor the given expression using the greatest common factor (GCF), we need to identify the term that all the terms in the expression have in common.
In this case, we can find the GCF by looking at the coefficients (the numbers in front of the variables) and the powers of the variable 'n'.
The coefficients of the terms in the expression are 12, 8, and 6. The powers of 'n' are 5, 3, and 1. To find the GCF of these numbers, we need to identify the largest number that can divide each coefficient evenly.
Let's start by finding the GCF of the coefficients: 12, 8, and 6.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 8 are 1, 2, 4, and 8.
The factors of 6 are 1, 2, 3, and 6.
From these lists, we can see that the largest number that divides all three coefficients evenly is 2.
Next, let's find the GCF of the powers of 'n': 5, 3, and 1.
The factors of 5 are 1 and 5.
The factors of 3 are 1 and 3.
The factor of 1 is 1.
Since the power of 'n' in the terms is different, the GCF of the powers is simply 1, since there is no common factor.
Now, to factor the expression using the GCF, we will factor out the GCF, which is 2n.
Taking out the GCF, the expression becomes:
2n(6n^4 + 4n^2 + 3)
Therefore, the factored form of the expression 12n^5 + 8n^3 + 6n using the greatest common factor is 2n(6n^4 + 4n^2 + 3).