Factor out the greatest common factor. Simplify if possible.
9x^6-63x^5+36x^4=
9x^4(x^2-7x+4)
To factor out the greatest common factor (GCF) in the expression 9x^6 - 63x^5 + 36x^4, we need to find the highest power of x that is common to all the terms.
Step 1: Identify the coefficients of each term (the numbers in front of the variables).
Coefficients: 9, -63, 36
Step 2: Find the highest power of x that appears in each term.
Powers of x: 6, 5, 4
Step 3: Determine the GCF by finding the smallest coefficient and the smallest power of x.
The GCF is 9x^4 because it is the largest common factor of all the terms.
Step 4: Divide each term by the GCF and write the simplified expression.
(9x^6)/(9x^4) - (63x^5)/(9x^4) + (36x^4)/(9x^4) = x^2 - 7x + 4
Therefore, the factored expression, after simplifying if possible, is x^2 - 7x + 4.