The length of a rectangular pan is represented by [tex]5a^2[/tex], and the area of the rectangular pan is represented by [tex]5a^4 + 10a^3 - 15a^2[/tex]. Find the polynomial expression that represents the width of the pan.

Write your answer in descending order.

Please use the palette below to enter your answer.

[tex]\boxed{}[/tex]



Answer :

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]