Answer :

To factor the expression [tex]\(20x^4 + 45x^5\)[/tex] completely, we can follow these steps:

1. Identify and Factor Out the Greatest Common Factor (GCF):

First, check if there is a common factor in all the terms.

- The coefficients are 20 and 45. The GCF of 20 and 45 is 5.
- For the variable part, both terms have a power of [tex]\(x\)[/tex]. The smallest power is [tex]\(x^4\)[/tex].

So, the GCF of the entire expression [tex]\(20x^4 + 45x^5\)[/tex] is [tex]\(5x^4\)[/tex].

2. Factor Out the GCF:

We can factor out [tex]\(5x^4\)[/tex] from each term in the expression:

[tex]\[
20x^4 + 45x^5 = 5x^4(4) + 5x^4(9x)
\][/tex]

Simplifying inside the parentheses:

[tex]\[
20x^4 + 45x^5 = 5x^4(4) + 5x^4(9x) = 5x^4(4 + 9x)
\][/tex]

3. Write the Final Factored Form:

The completely factored form of the expression is:

[tex]\[
5x^4(9x + 4)
\][/tex]

That's it! The expression [tex]\(20x^4 + 45x^5\)[/tex] is factored completely as [tex]\(5x^4(9x + 4)\)[/tex].

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