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Simplifying f(x) = (x7 + -4x6)(x + 3)(x + -2) Multiply f * x fx = (x7 + -4x6)(x + 3)(x + -2) Reorder the terms: fx = (-4x6 + x7)(x + 3)(x + -2) Reorder the terms: fx = (-4x6 + x7)(3 + x)(x + -2) Reorder the terms: fx = (-4x6 + x7)(3 + x)(-2 + x) Multiply (-4x6 + x7) * (3 + x) fx = (-4x6 * (3 + x) + x7(3 + x))(-2 + x) fx = ((3 * -4x6 + x * -4x6) + x7(3 + x))(-2 + x) fx = ((-12x6 + -4x7) + x7(3 + x))(-2 + x) fx = (-12x6 + -4x7 + (3 * x7 + x * x7))(-2 + x) fx = (-12x6 + -4x7 + (3x7 + x8))(-2 + x) Combine like terms: -4x7 + 3x7 = -1x7 fx = (-12x6 + -1x7 + x8)(-2 + x) Multiply (-12x6 + -1x7 + x8) * (-2 + x) fx = (-12x6 * (-2 + x) + -1x7 * (-2 + x) + x8(-2 + x)) fx = ((-2 * -12x6 + x * -12x6) + -1x7 * (-2 + x) + x8(-2 + x)) fx = ((24x6 + -12x7) + -1x7 * (-2 + x) + x8(-2 + x)) fx = (24x6 + -12x7 + (-2 * -1x7 + x * -1x7) + x8(-2 + x)) fx = (24x6 + -12x7 + (2x7 + -1x8) + x8(-2 + x)) fx = (24x6 + -12x7 + 2x7 + -1x8 + (-2 * x8 + x * x8)) fx = (24x6 + -12x7 + 2x7 + -1x8 + (-2x8 + x9)) Combine like terms: -12x7 + 2x7 = -10x7 fx = (24x6 + -10x7 + -1x8 + -2x8 + x9) Combine like terms: -1x8 + -2x8 = -3x8 fx = (24x6 + -10x7 + -3x8 + x9) Solving fx = 24x6 + -10x7 + -3x8 + x9 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 24x5 + -10x6 + -3x7 + x8 Simplifying f = 24x5 + -10x6 + -3x7 + x8
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