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Simplifying (fxg)(x) = (4x2 + -10x + 4)(x + -2) Multiply fgx * x fgx2 = (4x2 + -10x + 4)(x + -2) Reorder the terms: fgx2 = (4 + -10x + 4x2)(x + -2) Reorder the terms: fgx2 = (4 + -10x + 4x2)(-2 + x) Multiply (4 + -10x + 4x2) * (-2 + x) fgx2 = (4(-2 + x) + -10x * (-2 + x) + 4x2 * (-2 + x)) fgx2 = ((-2 * 4 + x * 4) + -10x * (-2 + x) + 4x2 * (-2 + x)) fgx2 = ((-8 + 4x) + -10x * (-2 + x) + 4x2 * (-2 + x)) fgx2 = (-8 + 4x + (-2 * -10x + x * -10x) + 4x2 * (-2 + x)) fgx2 = (-8 + 4x + (20x + -10x2) + 4x2 * (-2 + x)) fgx2 = (-8 + 4x + 20x + -10x2 + (-2 * 4x2 + x * 4x2)) fgx2 = (-8 + 4x + 20x + -10x2 + (-8x2 + 4x3)) Combine like terms: 4x + 20x = 24x fgx2 = (-8 + 24x + -10x2 + -8x2 + 4x3) Combine like terms: -10x2 + -8x2 = -18x2 fgx2 = (-8 + 24x + -18x2 + 4x3) Solving fgx2 = -8 + 24x + -18x2 + 4x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx2'. f = -8g-1x-2 + 24g-1x-1 + -18g-1 + 4g-1x Simplifying f = -8g-1x-2 + 24g-1x-1 + -18g-1 + 4g-1x Reorder the terms: f = -18g-1 + -8g-1x-2 + 24g-1x-1 + 4g-1x
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