what is the factor by removing the greatest common factor for x12-6x5, step by step
Online "^" is used to indicate an exponent.
x^12 - 6x^5 = x^5(x^7 - 6)
To factor out the greatest common factor (GCF) from the given expression x^12 - 6x^5, you need to identify the common factors of the two terms and then remove them from each term. Here's how you can do it step by step:
Step 1: Determine the GCF.
To find the GCF, look for the highest power of x that divides both terms. In this case, the highest power of x that can be divided from both terms is x^5.
Step 2: Divide each term by the GCF.
Divide each term by the GCF (x^5) to factor it out.
For the first term, x^12 ÷ x^5 = x^(12-5) = x^7.
For the second term, -6x^5 ÷ x^5 = -6.
Step 3: Write the factored expression.
Now that you have factored out the GCF, you can express the original polynomial as the product of the GCF and the remaining terms.
The factored expression for x^12 - 6x^5 is:
x^5(x^7 - 6).