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Simplifying f(x) = (x + 1)(x + 5)(5x + -1) Multiply f * x fx = (x + 1)(x + 5)(5x + -1) Reorder the terms: fx = (1 + x)(x + 5)(5x + -1) Reorder the terms: fx = (1 + x)(5 + x)(5x + -1) Reorder the terms: fx = (1 + x)(5 + x)(-1 + 5x) Multiply (1 + x) * (5 + x) fx = (1(5 + x) + x(5 + x))(-1 + 5x) fx = ((5 * 1 + x * 1) + x(5 + x))(-1 + 5x) fx = ((5 + 1x) + x(5 + x))(-1 + 5x) fx = (5 + 1x + (5 * x + x * x))(-1 + 5x) fx = (5 + 1x + (5x + x2))(-1 + 5x) Combine like terms: 1x + 5x = 6x fx = (5 + 6x + x2)(-1 + 5x) Multiply (5 + 6x + x2) * (-1 + 5x) fx = (5(-1 + 5x) + 6x * (-1 + 5x) + x2(-1 + 5x)) fx = ((-1 * 5 + 5x * 5) + 6x * (-1 + 5x) + x2(-1 + 5x)) fx = ((-5 + 25x) + 6x * (-1 + 5x) + x2(-1 + 5x)) fx = (-5 + 25x + (-1 * 6x + 5x * 6x) + x2(-1 + 5x)) fx = (-5 + 25x + (-6x + 30x2) + x2(-1 + 5x)) fx = (-5 + 25x + -6x + 30x2 + (-1 * x2 + 5x * x2)) fx = (-5 + 25x + -6x + 30x2 + (-1x2 + 5x3)) Combine like terms: 25x + -6x = 19x fx = (-5 + 19x + 30x2 + -1x2 + 5x3) Combine like terms: 30x2 + -1x2 = 29x2 fx = (-5 + 19x + 29x2 + 5x3) Solving fx = -5 + 19x + 29x2 + 5x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -5x-1 + 19 + 29x + 5x2 Simplifying f = -5x-1 + 19 + 29x + 5x2 Reorder the terms: f = 19 + -5x-1 + 29x + 5x2
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