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Simplifying f(x) = (x2 + 3x + -1)(2x2 + -5x + 1) Multiply f * x fx = (x2 + 3x + -1)(2x2 + -5x + 1) Reorder the terms: fx = (-1 + 3x + x2)(2x2 + -5x + 1) Reorder the terms: fx = (-1 + 3x + x2)(1 + -5x + 2x2) Multiply (-1 + 3x + x2) * (1 + -5x + 2x2) fx = (-1(1 + -5x + 2x2) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2)) fx = ((1 * -1 + -5x * -1 + 2x2 * -1) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2)) fx = ((-1 + 5x + -2x2) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2)) fx = (-1 + 5x + -2x2 + (1 * 3x + -5x * 3x + 2x2 * 3x) + x2(1 + -5x + 2x2)) fx = (-1 + 5x + -2x2 + (3x + -15x2 + 6x3) + x2(1 + -5x + 2x2)) fx = (-1 + 5x + -2x2 + 3x + -15x2 + 6x3 + (1 * x2 + -5x * x2 + 2x2 * x2)) fx = (-1 + 5x + -2x2 + 3x + -15x2 + 6x3 + (1x2 + -5x3 + 2x4)) Reorder the terms: fx = (-1 + 5x + 3x + -2x2 + -15x2 + 1x2 + 6x3 + -5x3 + 2x4) Combine like terms: 5x + 3x = 8x fx = (-1 + 8x + -2x2 + -15x2 + 1x2 + 6x3 + -5x3 + 2x4) Combine like terms: -2x2 + -15x2 = -17x2 fx = (-1 + 8x + -17x2 + 1x2 + 6x3 + -5x3 + 2x4) Combine like terms: -17x2 + 1x2 = -16x2 fx = (-1 + 8x + -16x2 + 6x3 + -5x3 + 2x4) Combine like terms: 6x3 + -5x3 = 1x3 fx = (-1 + 8x + -16x2 + 1x3 + 2x4) Solving fx = -1 + 8x + -16x2 + 1x3 + 2x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -1x-1 + 8 + -16x + x2 + 2x3 Simplifying f = -1x-1 + 8 + -16x + x2 + 2x3 Reorder the terms: f = 8 + -1x-1 + -16x + x2 + 2x3
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