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28 January, 12:29

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?

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  1. 28 January, 14:35
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    10r⁵ + 2r⁴ + 5r²

    Step-by-step 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.
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