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Simplifying f(x) = (t + -2)(t + -2)(t + -2) + -1(t + -2) Multiply f * x fx = (t + -2)(t + -2)(t + -2) + -1(t + -2) Reorder the terms: fx = (-2 + t)(t + -2)(t + -2) + -1(t + -2) Reorder the terms: fx = (-2 + t)(-2 + t)(t + -2) + -1(t + -2) Reorder the terms: fx = (-2 + t)(-2 + t)(-2 + t) + -1(t + -2) Multiply (-2 + t) * (-2 + t) fx = (-2(-2 + t) + t(-2 + t))(-2 + t) + -1(t + -2) fx = ((-2 * -2 + t * -2) + t(-2 + t))(-2 + t) + -1(t + -2) fx = ((4 + -2t) + t(-2 + t))(-2 + t) + -1(t + -2) fx = (4 + -2t + (-2 * t + t * t))(-2 + t) + -1(t + -2) fx = (4 + -2t + (-2t + t2))(-2 + t) + -1(t + -2) Combine like terms: -2t + -2t = -4t fx = (4 + -4t + t2)(-2 + t) + -1(t + -2) Multiply (4 + -4t + t2) * (-2 + t) fx = (4(-2 + t) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2) fx = ((-2 * 4 + t * 4) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2) fx = ((-8 + 4t) + -4t * (-2 + t) + t2(-2 + t)) + -1(t + -2) fx = (-8 + 4t + (-2 * -4t + t * -4t) + t2(-2 + t)) + -1(t + -2) fx = (-8 + 4t + (8t + -4t2) + t2(-2 + t)) + -1(t + -2) fx = (-8 + 4t + 8t + -4t2 + (-2 * t2 + t * t2)) + -1(t + -2) fx = (-8 + 4t + 8t + -4t2 + (-2t2 + t3)) + -1(t + -2) Combine like terms: 4t + 8t = 12t fx = (-8 + 12t + -4t2 + -2t2 + t3) + -1(t + -2) Combine like terms: -4t2 + -2t2 = -6t2 fx = (-8 + 12t + -6t2 + t3) + -1(t + -2) Reorder the terms: fx = -8 + 12t + -6t2 + t3 + -1(-2 + t) fx = -8 + 12t + -6t2 + t3 + (-2 * -1 + t * -1) fx = -8 + 12t + -6t2 + t3 + (2 + -1t) Reorder the terms: fx = -8 + 2 + 12t + -1t + -6t2 + t3 Combine like terms: -8 + 2 = -6 fx = -6 + 12t + -1t + -6t2 + t3 Combine like terms: 12t + -1t = 11t fx = -6 + 11t + -6t2 + t3 Solving fx = -6 + 11t + -6t2 + t3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = -6x-1 + 11tx-1 + -6t2x-1 + t3x-1 Simplifying f = -6x-1 + 11tx-1 + -6t2x-1 + t3x-1 Reorder the terms: f = 11tx-1 + -6t2x-1 + t3x-1 + -6x-1
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