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Simplifying f(x) = (x2 + 11x + 7)(5x4 + -3x2) Multiply f * x fx = (x2 + 11x + 7)(5x4 + -3x2) Reorder the terms: fx = (7 + 11x + x2)(5x4 + -3x2) Reorder the terms: fx = (7 + 11x + x2)(-3x2 + 5x4) Multiply (7 + 11x + x2) * (-3x2 + 5x4) fx = (7(-3x2 + 5x4) + 11x * (-3x2 + 5x4) + x2(-3x2 + 5x4)) fx = ((-3x2 * 7 + 5x4 * 7) + 11x * (-3x2 + 5x4) + x2(-3x2 + 5x4)) fx = ((-21x2 + 35x4) + 11x * (-3x2 + 5x4) + x2(-3x2 + 5x4)) fx = (-21x2 + 35x4 + (-3x2 * 11x + 5x4 * 11x) + x2(-3x2 + 5x4)) fx = (-21x2 + 35x4 + (-33x3 + 55x5) + x2(-3x2 + 5x4)) fx = (-21x2 + 35x4 + -33x3 + 55x5 + (-3x2 * x2 + 5x4 * x2)) fx = (-21x2 + 35x4 + -33x3 + 55x5 + (-3x4 + 5x6)) Reorder the terms: fx = (-21x2 + -33x3 + 35x4 + -3x4 + 55x5 + 5x6) Combine like terms: 35x4 + -3x4 = 32x4 fx = (-21x2 + -33x3 + 32x4 + 55x5 + 5x6) Solving fx = -21x2 + -33x3 + 32x4 + 55x5 + 5x6 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -21x + -33x2 + 32x3 + 55x4 + 5x5 Simplifying f = -21x + -33x2 + 32x3 + 55x4 + 5x5
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