Answer :

We are given the expression

[tex]$$
20x^4 + 45x^5.
$$[/tex]

Step 1. Identify the Greatest Common Factor (GCF):

Look at the two terms:

- The first term is [tex]$20x^4$[/tex].
- The second term is [tex]$45x^5$[/tex].

For the numerical coefficients, the GCF of [tex]$20$[/tex] and [tex]$45$[/tex] is [tex]$5$[/tex]. For the variable part, the smallest power of [tex]$x$[/tex] that appears in both terms is [tex]$x^4$[/tex]. Therefore, the overall GCF is

[tex]$$
5x^4.
$$[/tex]

Step 2. Factor out the GCF from the Expression:

Divide each term by [tex]$5x^4$[/tex]:

- For [tex]$20x^4$[/tex], we have:
[tex]$$
\frac{20x^4}{5x^4} = 4.
$$[/tex]
- For [tex]$45x^5$[/tex], we have:
[tex]$$
\frac{45x^5}{5x^4} = 9x.
$$[/tex]

Thus, factoring [tex]$5x^4$[/tex] out of the expression yields:

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

Step 3. Write the Completely Factored Form:

The expression factored completely is:

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

Note that since addition is commutative, [tex]$4 + 9x$[/tex] can also be written as [tex]$9x + 4$[/tex].

So, the final completely factored form is:

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

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