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Simplifying h(x) = (x + 1)(x + 3)(2x + -3) Multiply h * x hx = (x + 1)(x + 3)(2x + -3) Reorder the terms: hx = (1 + x)(x + 3)(2x + -3) Reorder the terms: hx = (1 + x)(3 + x)(2x + -3) Reorder the terms: hx = (1 + x)(3 + x)(-3 + 2x) Multiply (1 + x) * (3 + x) hx = (1(3 + x) + x(3 + x))(-3 + 2x) hx = ((3 * 1 + x * 1) + x(3 + x))(-3 + 2x) hx = ((3 + 1x) + x(3 + x))(-3 + 2x) hx = (3 + 1x + (3 * x + x * x))(-3 + 2x) hx = (3 + 1x + (3x + x2))(-3 + 2x) Combine like terms: 1x + 3x = 4x hx = (3 + 4x + x2)(-3 + 2x) Multiply (3 + 4x + x2) * (-3 + 2x) hx = (3(-3 + 2x) + 4x * (-3 + 2x) + x2(-3 + 2x)) hx = ((-3 * 3 + 2x * 3) + 4x * (-3 + 2x) + x2(-3 + 2x)) hx = ((-9 + 6x) + 4x * (-3 + 2x) + x2(-3 + 2x)) hx = (-9 + 6x + (-3 * 4x + 2x * 4x) + x2(-3 + 2x)) hx = (-9 + 6x + (-12x + 8x2) + x2(-3 + 2x)) hx = (-9 + 6x + -12x + 8x2 + (-3 * x2 + 2x * x2)) hx = (-9 + 6x + -12x + 8x2 + (-3x2 + 2x3)) Combine like terms: 6x + -12x = -6x hx = (-9 + -6x + 8x2 + -3x2 + 2x3) Combine like terms: 8x2 + -3x2 = 5x2 hx = (-9 + -6x + 5x2 + 2x3) Solving hx = -9 + -6x + 5x2 + 2x3 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 'x'. h = -9x-1 + -6 + 5x + 2x2 Simplifying h = -9x-1 + -6 + 5x + 2x2 Reorder the terms: h = -6 + -9x-1 + 5x + 2x2
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