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Simplifying h(x) = x(x + -1)(x + 2)(x + -4) Multiply h * x hx = x(x + -1)(x + 2)(x + -4) Reorder the terms: hx = x(-1 + x)(x + 2)(x + -4) Reorder the terms: hx = x(-1 + x)(2 + x)(x + -4) Reorder the terms: hx = x(-1 + x)(2 + x)(-4 + x) Multiply (-1 + x) * (2 + x) hx = x(-1(2 + x) + x(2 + x))(-4 + x) hx = x((2 * -1 + x * -1) + x(2 + x))(-4 + x) hx = x((-2 + -1x) + x(2 + x))(-4 + x) hx = x(-2 + -1x + (2 * x + x * x))(-4 + x) hx = x(-2 + -1x + (2x + x2))(-4 + x) Combine like terms: -1x + 2x = 1x hx = x(-2 + 1x + x2)(-4 + x) Multiply (-2 + 1x + x2) * (-4 + x) hx = x(-2(-4 + x) + 1x * (-4 + x) + x2(-4 + x)) hx = x((-4 * -2 + x * -2) + 1x * (-4 + x) + x2(-4 + x)) hx = x((8 + -2x) + 1x * (-4 + x) + x2(-4 + x)) hx = x(8 + -2x + (-4 * 1x + x * 1x) + x2(-4 + x)) hx = x(8 + -2x + (-4x + 1x2) + x2(-4 + x)) hx = x(8 + -2x + -4x + 1x2 + (-4 * x2 + x * x2)) hx = x(8 + -2x + -4x + 1x2 + (-4x2 + x3)) Combine like terms: -2x + -4x = -6x hx = x(8 + -6x + 1x2 + -4x2 + x3) Combine like terms: 1x2 + -4x2 = -3x2 hx = x(8 + -6x + -3x2 + x3) hx = (8 * x + -6x * x + -3x2 * x + x3 * x) hx = (8x + -6x2 + -3x3 + x4) Solving hx = 8x + -6x2 + -3x3 + x4 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 'x'. h = 8 + -6x + -3x2 + x3 Simplifying h = 8 + -6x + -3x2 + x3
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