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Simplifying h(x) = (x2 + -3x + 2)(2x3 + 1) Multiply h * x hx = (x2 + -3x + 2)(2x3 + 1) Reorder the terms: hx = (2 + -3x + x2)(2x3 + 1) Reorder the terms: hx = (2 + -3x + x2)(1 + 2x3) Multiply (2 + -3x + x2) * (1 + 2x3) hx = (2(1 + 2x3) + -3x * (1 + 2x3) + x2(1 + 2x3)) hx = ((1 * 2 + 2x3 * 2) + -3x * (1 + 2x3) + x2(1 + 2x3)) hx = ((2 + 4x3) + -3x * (1 + 2x3) + x2(1 + 2x3)) hx = (2 + 4x3 + (1 * -3x + 2x3 * -3x) + x2(1 + 2x3)) hx = (2 + 4x3 + (-3x + -6x4) + x2(1 + 2x3)) hx = (2 + 4x3 + -3x + -6x4 + (1 * x2 + 2x3 * x2)) hx = (2 + 4x3 + -3x + -6x4 + (1x2 + 2x5)) Reorder the terms: hx = (2 + -3x + 1x2 + 4x3 + -6x4 + 2x5) hx = (2 + -3x + 1x2 + 4x3 + -6x4 + 2x5) Solving hx = 2 + -3x + 1x2 + 4x3 + -6x4 + 2x5 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 'x'. h = 2x-1 + -3 + x + 4x2 + -6x3 + 2x4 Simplifying h = 2x-1 + -3 + x + 4x2 + -6x3 + 2x4 Reorder the terms: h = -3 + 2x-1 + x + 4x2 + -6x3 + 2x4
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