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Factor out the greatest common factor from the polynomial [tex]$45x^5 + 36x^3$[/tex].

If the greatest common factor is 1, just retype the polynomial.

Answer :

Sure! Let's factor out the greatest common factor from the polynomial [tex]\(45x^5 + 36x^3\)[/tex].

1. Identify the coefficients and powers of [tex]\(x\)[/tex]:

The polynomial is made up of two terms:
- The first term is [tex]\(45x^5\)[/tex], with a coefficient of 45.
- The second term is [tex]\(36x^3\)[/tex], with a coefficient of 36.

2. Find the greatest common factor (GCF) of the coefficients:

To find the GCF of the numbers 45 and 36, we need to list out their factors:
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The greatest common factor is the largest number that appears in both lists. Here, it is 9.

3. Factor the GCF from each term:

We will divide each term by the GCF, which is 9:
- [tex]\(45x^5 ÷ 9 = 5x^5\)[/tex]
- [tex]\(36x^3 ÷ 9 = 4x^3\)[/tex]

4. Write the factored form:

Now, express the polynomial by factoring out the GCF:

[tex]\[
45x^5 + 36x^3 = 9(5x^5 + 4x^3)
\][/tex]

So, the factored form of the polynomial is [tex]\(9(5x^5 + 4x^3)\)[/tex].

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