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Simplifying f(x) = -5(x + 4)(x3 + -12x2 + 48x + -64) Multiply f * x fx = -5(x + 4)(x3 + -12x2 + 48x + -64) Reorder the terms: fx = -5(4 + x)(x3 + -12x2 + 48x + -64) Reorder the terms: fx = -5(4 + x)(-64 + 48x + -12x2 + x3) Multiply (4 + x) * (-64 + 48x + -12x2 + x3) fx = -5(4(-64 + 48x + -12x2 + x3) + x(-64 + 48x + -12x2 + x3)) fx = -5((-64 * 4 + 48x * 4 + -12x2 * 4 + x3 * 4) + x(-64 + 48x + -12x2 + x3)) fx = -5((-256 + 192x + -48x2 + 4x3) + x(-64 + 48x + -12x2 + x3)) fx = -5(-256 + 192x + -48x2 + 4x3 + (-64 * x + 48x * x + -12x2 * x + x3 * x)) fx = -5(-256 + 192x + -48x2 + 4x3 + (-64x + 48x2 + -12x3 + x4)) Reorder the terms: fx = -5(-256 + 192x + -64x + -48x2 + 48x2 + 4x3 + -12x3 + x4) Combine like terms: 192x + -64x = 128x fx = -5(-256 + 128x + -48x2 + 48x2 + 4x3 + -12x3 + x4) Combine like terms: -48x2 + 48x2 = 0 fx = -5(-256 + 128x + 0 + 4x3 + -12x3 + x4) fx = -5(-256 + 128x + 4x3 + -12x3 + x4) Combine like terms: 4x3 + -12x3 = -8x3 fx = -5(-256 + 128x + -8x3 + x4) fx = (-256 * -5 + 128x * -5 + -8x3 * -5 + x4 * -5) fx = (1280 + -640x + 40x3 + -5x4) Solving fx = 1280 + -640x + 40x3 + -5x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 1280x-1 + -640 + 40x2 + -5x3 Simplifying f = 1280x-1 + -640 + 40x2 + -5x3 Reorder the terms: f = -640 + 1280x-1 + 40x2 + -5x3
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