Suppose the width of a rectangle is #2b - 1# and the area is #4b^3 + 5b - 3#. What is the length of the rectangle?

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Answer 1 · 2016-06-20T14:36:55

The formula for area of a rectangle is #A = L xx W#.

Therefore #A/W = L#, and by continuation #2b - 1# must be a factor of#4b^3+ 5b - 3#.

By synthetic division:

#1/2"_|4 0 5 -3"#
#" 2 1 3"#
#"-------------------------"#
#" 4 2 6 0"#

Hence, #(4b^3 + 5b - 3)/(2b - 1)# gives a quotient of #4b^2 + 2b+ 6#.

#:.# The length of the rectangle measures #(4b^2 + 2b+ 6)# inches.

Hopefully this helps!