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Simplifying h(x) = x(x + -2)(x + 3)(x + -8) Multiply h * x hx = x(x + -2)(x + 3)(x + -8) Reorder the terms: hx = x(-2 + x)(x + 3)(x + -8) Reorder the terms: hx = x(-2 + x)(3 + x)(x + -8) Reorder the terms: hx = x(-2 + x)(3 + x)(-8 + x) Multiply (-2 + x) * (3 + x) hx = x(-2(3 + x) + x(3 + x))(-8 + x) hx = x((3 * -2 + x * -2) + x(3 + x))(-8 + x) hx = x((-6 + -2x) + x(3 + x))(-8 + x) hx = x(-6 + -2x + (3 * x + x * x))(-8 + x) hx = x(-6 + -2x + (3x + x2))(-8 + x) Combine like terms: -2x + 3x = 1x hx = x(-6 + 1x + x2)(-8 + x) Multiply (-6 + 1x + x2) * (-8 + x) hx = x(-6(-8 + x) + 1x * (-8 + x) + x2(-8 + x)) hx = x((-8 * -6 + x * -6) + 1x * (-8 + x) + x2(-8 + x)) hx = x((48 + -6x) + 1x * (-8 + x) + x2(-8 + x)) hx = x(48 + -6x + (-8 * 1x + x * 1x) + x2(-8 + x)) hx = x(48 + -6x + (-8x + 1x2) + x2(-8 + x)) hx = x(48 + -6x + -8x + 1x2 + (-8 * x2 + x * x2)) hx = x(48 + -6x + -8x + 1x2 + (-8x2 + x3)) Combine like terms: -6x + -8x = -14x hx = x(48 + -14x + 1x2 + -8x2 + x3) Combine like terms: 1x2 + -8x2 = -7x2 hx = x(48 + -14x + -7x2 + x3) hx = (48 * x + -14x * x + -7x2 * x + x3 * x) hx = (48x + -14x2 + -7x3 + x4) Solving hx = 48x + -14x2 + -7x3 + 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 = 48 + -14x + -7x2 + x3 Simplifying h = 48 + -14x + -7x2 + x3
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