Answer:
10r⁵ + 2r⁴ + 5r²
Explanation:
A = 90r⁶ + 28r⁵ + 2r⁴ + 45r³ + 5r²
Factor our r²:
A = r² (90r⁴ + 28r³ + 2r² + 45r + 5)
Factor 2r² from the first three terms and 5 from the last two:
A = r² (2r² (45r² + 14r + 1) + 5 (9r + 1))
Factor the trinomial:
A = r² (2r² (5r + 1)(9r + 1) + 5 (9r + 1))
Factor out 9r+1:
A = r² (2r² (5r + 1) + 5) (9r + 1)
Distribute the 2r²:
A = r² (10r³ + 2r² + 5) (9r + 1)
Distribute the r²:
A = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
The area is width times length, and the width is 9r + 1.
WL = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
(9r + 1) L = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
L = 10r⁵ + 2r⁴ + 5r²
The length of the pool is 10r⁵ + 2r⁴ + 5r².