We divide the given quadratic area expression by the given width binomial. Factoring the numerator 2x square + 7x + 3 yields (2x + 1)(x + 3) and cancelling the common width factor leaves the length.
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: Setting up the equation as x + 1/x = 10/3 creates a quadratic form 3x square – 10x + 3 = 0. Factoring this gives (3x – 1)(x – 3) = 0, which provides the two possible numerical answers.
The total outer side length including the path becomes 40 + 2s metres. Subtracting the inner square area (1600) from the expanded outer square area provides the final algebraic expression for the path.
We factor out the common algebraic term 3p from the expression. The remaining quadratic part inside the brackets is s square – 5s + 4, which is split into the linear binomial factors (s – 1) and (s – 4).
We first take out the common constant factor 6 from the volume expression. This leaves a square – 4b square inside brackets, which breaks down further into (a + 2b)(a – 2b) using the difference of squares formula.