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Simplifying f(x) = a(x + 3)(x + 1)(x + -4) Multiply f * x fx = a(x + 3)(x + 1)(x + -4) Reorder the terms: fx = a(3 + x)(x + 1)(x + -4) Reorder the terms: fx = a(3 + x)(1 + x)(x + -4) Reorder the terms: fx = a(3 + x)(1 + x)(-4 + x) Multiply (3 + x) * (1 + x) fx = a(3(1 + x) + x(1 + x))(-4 + x) fx = a((1 * 3 + x * 3) + x(1 + x))(-4 + x) fx = a((3 + 3x) + x(1 + x))(-4 + x) fx = a(3 + 3x + (1 * x + x * x))(-4 + x) fx = a(3 + 3x + (1x + x2))(-4 + x) Combine like terms: 3x + 1x = 4x fx = a(3 + 4x + x2)(-4 + x) Multiply (3 + 4x + x2) * (-4 + x) fx = a(3(-4 + x) + 4x * (-4 + x) + x2(-4 + x)) fx = a((-4 * 3 + x * 3) + 4x * (-4 + x) + x2(-4 + x)) fx = a((-12 + 3x) + 4x * (-4 + x) + x2(-4 + x)) fx = a(-12 + 3x + (-4 * 4x + x * 4x) + x2(-4 + x)) fx = a(-12 + 3x + (-16x + 4x2) + x2(-4 + x)) fx = a(-12 + 3x + -16x + 4x2 + (-4 * x2 + x * x2)) fx = a(-12 + 3x + -16x + 4x2 + (-4x2 + x3)) Combine like terms: 3x + -16x = -13x fx = a(-12 + -13x + 4x2 + -4x2 + x3) Combine like terms: 4x2 + -4x2 = 0 fx = a(-12 + -13x + 0 + x3) fx = a(-12 + -13x + x3) fx = (-12 * a + -13x * a + x3 * a) fx = (-12a + -13ax + ax3) Solving fx = -12a + -13ax + ax3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -12ax-1 + -13a + ax2 Simplifying f = -12ax-1 + -13a + ax2 Reorder the terms: f = -13a + -12ax-1 + ax2
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