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Simplifying v(x) = (2x + 5)(2x + 7)(x + 4) Multiply v * x vx = (2x + 5)(2x + 7)(x + 4) Reorder the terms: vx = (5 + 2x)(2x + 7)(x + 4) Reorder the terms: vx = (5 + 2x)(7 + 2x)(x + 4) Reorder the terms: vx = (5 + 2x)(7 + 2x)(4 + x) Multiply (5 + 2x) * (7 + 2x) vx = (5(7 + 2x) + 2x * (7 + 2x))(4 + x) vx = ((7 * 5 + 2x * 5) + 2x * (7 + 2x))(4 + x) vx = ((35 + 10x) + 2x * (7 + 2x))(4 + x) vx = (35 + 10x + (7 * 2x + 2x * 2x))(4 + x) vx = (35 + 10x + (14x + 4x2))(4 + x) Combine like terms: 10x + 14x = 24x vx = (35 + 24x + 4x2)(4 + x) Multiply (35 + 24x + 4x2) * (4 + x) vx = (35(4 + x) + 24x * (4 + x) + 4x2 * (4 + x)) vx = ((4 * 35 + x * 35) + 24x * (4 + x) + 4x2 * (4 + x)) vx = ((140 + 35x) + 24x * (4 + x) + 4x2 * (4 + x)) vx = (140 + 35x + (4 * 24x + x * 24x) + 4x2 * (4 + x)) vx = (140 + 35x + (96x + 24x2) + 4x2 * (4 + x)) vx = (140 + 35x + 96x + 24x2 + (4 * 4x2 + x * 4x2)) vx = (140 + 35x + 96x + 24x2 + (16x2 + 4x3)) Combine like terms: 35x + 96x = 131x vx = (140 + 131x + 24x2 + 16x2 + 4x3) Combine like terms: 24x2 + 16x2 = 40x2 vx = (140 + 131x + 40x2 + 4x3) Solving vx = 140 + 131x + 40x2 + 4x3 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Divide each side by 'x'. v = 140x-1 + 131 + 40x + 4x2 Simplifying v = 140x-1 + 131 + 40x + 4x2 Reorder the terms: v = 131 + 140x-1 + 40x + 4x2
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