Q:

The width, w, of a rectangular swimming pool 9r + 1. The area A of the pool is 90r^6+28r^5+2r^(4 )+ 45r^3+5r^2. What is an expression for the length of the pool?

Accepted Solution

A:
Answer:10r⁵ + 2r⁴ + 5r²Step-by-step explanation:A = 90r⁶ + 28r⁵ + 2r⁴ + 45r³ + 5r²Factor 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 + 5r²The length of the pool is 10r⁵ + 2r⁴ + 5r².