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Simplifying f(x) = (x + -8)(4x + 2)(3x + -8) Multiply f * x fx = (x + -8)(4x + 2)(3x + -8) Reorder the terms: fx = (-8 + x)(4x + 2)(3x + -8) Reorder the terms: fx = (-8 + x)(2 + 4x)(3x + -8) Reorder the terms: fx = (-8 + x)(2 + 4x)(-8 + 3x) Multiply (-8 + x) * (2 + 4x) fx = (-8(2 + 4x) + x(2 + 4x))(-8 + 3x) fx = ((2 * -8 + 4x * -8) + x(2 + 4x))(-8 + 3x) fx = ((-16 + -32x) + x(2 + 4x))(-8 + 3x) fx = (-16 + -32x + (2 * x + 4x * x))(-8 + 3x) fx = (-16 + -32x + (2x + 4x2))(-8 + 3x) Combine like terms: -32x + 2x = -30x fx = (-16 + -30x + 4x2)(-8 + 3x) Multiply (-16 + -30x + 4x2) * (-8 + 3x) fx = (-16(-8 + 3x) + -30x * (-8 + 3x) + 4x2 * (-8 + 3x)) fx = ((-8 * -16 + 3x * -16) + -30x * (-8 + 3x) + 4x2 * (-8 + 3x)) fx = ((128 + -48x) + -30x * (-8 + 3x) + 4x2 * (-8 + 3x)) fx = (128 + -48x + (-8 * -30x + 3x * -30x) + 4x2 * (-8 + 3x)) fx = (128 + -48x + (240x + -90x2) + 4x2 * (-8 + 3x)) fx = (128 + -48x + 240x + -90x2 + (-8 * 4x2 + 3x * 4x2)) fx = (128 + -48x + 240x + -90x2 + (-32x2 + 12x3)) Combine like terms: -48x + 240x = 192x fx = (128 + 192x + -90x2 + -32x2 + 12x3) Combine like terms: -90x2 + -32x2 = -122x2 fx = (128 + 192x + -122x2 + 12x3) Solving fx = 128 + 192x + -122x2 + 12x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 128x-1 + 192 + -122x + 12x2 Simplifying f = 128x-1 + 192 + -122x + 12x2 Reorder the terms: f = 192 + 128x-1 + -122x + 12x2
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