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Simplifying h(x) = (x + 4)(x + -6)(x + -8) Multiply h * x hx = (x + 4)(x + -6)(x + -8) Reorder the terms: hx = (4 + x)(x + -6)(x + -8) Reorder the terms: hx = (4 + x)(-6 + x)(x + -8) Reorder the terms: hx = (4 + x)(-6 + x)(-8 + x) Multiply (4 + x) * (-6 + x) hx = (4(-6 + x) + x(-6 + x))(-8 + x) hx = ((-6 * 4 + x * 4) + x(-6 + x))(-8 + x) hx = ((-24 + 4x) + x(-6 + x))(-8 + x) hx = (-24 + 4x + (-6 * x + x * x))(-8 + x) hx = (-24 + 4x + (-6x + x2))(-8 + x) Combine like terms: 4x + -6x = -2x hx = (-24 + -2x + x2)(-8 + x) Multiply (-24 + -2x + x2) * (-8 + x) hx = (-24(-8 + x) + -2x * (-8 + x) + x2(-8 + x)) hx = ((-8 * -24 + x * -24) + -2x * (-8 + x) + x2(-8 + x)) hx = ((192 + -24x) + -2x * (-8 + x) + x2(-8 + x)) hx = (192 + -24x + (-8 * -2x + x * -2x) + x2(-8 + x)) hx = (192 + -24x + (16x + -2x2) + x2(-8 + x)) hx = (192 + -24x + 16x + -2x2 + (-8 * x2 + x * x2)) hx = (192 + -24x + 16x + -2x2 + (-8x2 + x3)) Combine like terms: -24x + 16x = -8x hx = (192 + -8x + -2x2 + -8x2 + x3) Combine like terms: -2x2 + -8x2 = -10x2 hx = (192 + -8x + -10x2 + x3) Solving hx = 192 + -8x + -10x2 + x3 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 'x'. h = 192x-1 + -8 + -10x + x2 Simplifying h = 192x-1 + -8 + -10x + x2 Reorder the terms: h = -8 + 192x-1 + -10x + x2
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