College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Find the complete factored form of the polynomial:

[tex]-40 a^6 b^6 + 25 a^2 b^5[/tex]

Enter the correct answer.

Answer :

Let's find the complete factored form of the polynomial [tex]\(-40 a^6 b^6 + 25 a^2 b^5\)[/tex].

1. Identify the Greatest Common Factor (GCF):
First, we'll look for the greatest common factor of the two terms.

- For the coefficients: The GCF of 40 and 25 is 5.
- For the variables:
- The smallest power of [tex]\(a\)[/tex] present in both terms is [tex]\(a^2\)[/tex].
- The smallest power of [tex]\(b\)[/tex] present in both terms is [tex]\(b^5\)[/tex].

Therefore, the GCF of the entire expression is [tex]\(5a^2b^5\)[/tex].

2. Factor out the GCF from the polynomial:
We factor out [tex]\(5a^2b^5\)[/tex] from each term:

[tex]\[
-40a^6b^6 + 25a^2b^5 = -5a^2b^5(8a^4b - 5)
\][/tex]

- From [tex]\(-40a^6b^6\)[/tex]:
[tex]\[
\frac{-40a^6b^6}{5a^2b^5} = -8a^4b
\][/tex]

- From [tex]\(25a^2b^5\)[/tex]:
[tex]\[
\frac{25a^2b^5}{5a^2b^5} = 5
\][/tex]

3. Write the complete factored form:

Hence, the complete factored form of the polynomial is:
[tex]\[
-5a^2b^5(8a^4b - 5)
\][/tex]

This is the complete factored expression of the given polynomial.