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Simplifying f(x) = 1x3 + 2x5 + 1x7 + 0x2 + -1x7 + 9x2 + 9x5 + 8x4 Multiply f * x fx = 1x3 + 2x5 + 1x7 + 0x2 + -1x7 + 9x2 + 9x5 + 8x4 Anything times zero is zero. fx = 1x3 + 2x5 + 1x7 + 0x2 + -1x7 + 9x2 + 9x5 + 8x4 Reorder the terms: fx = 0 + 9x2 + 1x3 + 8x4 + 2x5 + 9x5 + 1x7 + -1x7 Remove the zero: fx = 9x2 + 1x3 + 8x4 + 2x5 + 9x5 + 1x7 + -1x7 Combine like terms: 2x5 + 9x5 = 11x5 fx = 9x2 + 1x3 + 8x4 + 11x5 + 1x7 + -1x7 Combine like terms: 1x7 + -1x7 = 0 fx = 9x2 + 1x3 + 8x4 + 11x5 + 0 fx = 9x2 + 1x3 + 8x4 + 11x5 Solving fx = 9x2 + 1x3 + 8x4 + 11x5 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 9x + x2 + 8x3 + 11x4 Simplifying f = 9x + x2 + 8x3 + 11x4
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