To find the width of the rectangular pan, we need to divide the area of the pan by its length.
1. The length of the rectangular pan is given by:
[tex]\[ L = 5a^2 \][/tex]
2. The area of the rectangular pan is given by:
[tex]\[ A = 5a^4 + 10a^3 - 15a^2 \][/tex]
3. The width [tex]\( W \)[/tex] can be calculated by dividing the area by the length:
[tex]\[ W = \frac{A}{L} = \frac{5a^4 + 10a^3 - 15a^2}{5a^2} \][/tex]
4. Divide each term in the numerator by the term in the denominator:
[tex]\[ W = \frac{5a^4}{5a^2} + \frac{10a^3}{5a^2} - \frac{15a^2}{5a^2} \][/tex]
5. Simplify each term:
[tex]\[ W = a^2 + 2a - 3 \][/tex]
Thus, the polynomial expression that represents the width of the rectangular pan is:
[tex]\[ \boxed{a^2 + 2a - 3} \][/tex]
