Let's find the greatest common divisor (GCD) of the polynomials [tex]\(3x^3 + 15x^2\)[/tex] and [tex]\(9x^2 + 59x\)[/tex].
### Step-by-Step Solution:
1. Factor each polynomial:
For the first polynomial [tex]\(3x^3 + 15x^2\)[/tex]:
[tex]\[
3x^3 + 15x^2 = 3x^2 (x + 5)
\][/tex]
For the second polynomial [tex]\(9x^2 + 59x\)[/tex]:
[tex]\[
9x^2 + 59x = x(9x + 59)
\][/tex]
2. Identify the common factors:
The factored forms of the polynomials are:
[tex]\[
3x^2 (x + 5) \quad \text{and} \quad x (9x + 59)
\][/tex]
The common factor in both factorizations is [tex]\(x\)[/tex].
Thus, the greatest common divisor (GCD) of the polynomials [tex]\(3x^3 + 15x^2\)[/tex] and [tex]\(9x^2 + 59x\)[/tex] is:
[tex]\[
\boxed{x}
\][/tex]
