Question

factor out the greatest common factor from the following polynomial.
$9x^7 - 81x^6 + 36x^5$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $9x^7 - 81x^6 + 36x^5 = \square$ (type your answer in factored form.)
b. the polynomial has no common factor other than 1.

Explanation:

Step1: Identify GCF of coefficients

Find GCF of 9, 81, 36:
$\gcd(9,81,36) = 9$

Step2: Identify GCF of variables

Find lowest power of $x$:
$x^5$ (since $5<6<7$)

Step3: Factor out GCF from each term

Divide each term by $9x^5$:
$9x^7 \div 9x^5 = x^2$, $-81x^6 \div 9x^5 = -9x$, $36x^5 \div 9x^5 = 4$

Step4: Write factored form

Combine GCF and remaining terms:
$9x^5(x^2 - 9x + 4)$

Answer:

A. $9x^7 - 81x^6 + 36x^5 = 9x^5(x^2 - 9x + 4)$