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Simplifying x2 + px + -9 = (x + -1)(x + q) Reorder the terms: -9 + px + x2 = (x + -1)(x + q) Reorder the terms: -9 + px + x2 = (-1 + x)(x + q) Reorder the terms: -9 + px + x2 = (-1 + x)(q + x) Multiply (-1 + x) * (q + x) -9 + px + x2 = (-1(q + x) + x(q + x)) -9 + px + x2 = ((q * -1 + x * -1) + x(q + x)) -9 + px + x2 = ((-1q + -1x) + x(q + x)) -9 + px + x2 = (-1q + -1x + (q * x + x * x)) -9 + px + x2 = (-1q + -1x + (qx + x2)) Reorder the terms: -9 + px + x2 = (-1q + qx + -1x + x2) -9 + px + x2 = (-1q + qx + -1x + x2) Add '-1x2' to each side of the equation. -9 + px + x2 + -1x2 = -1q + qx + -1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + px + 0 = -1q + qx + -1x + x2 + -1x2 -9 + px = -1q + qx + -1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + px = -1q + qx + -1x + 0 -9 + px = -1q + qx + -1x Solving -9 + px = -1q + qx + -1x Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + px = -1q + qx + 9 + -1x Combine like terms: -9 + 9 = 0 0 + px = -1q + qx + 9 + -1x px = -1q + qx + 9 + -1x Reorder the terms: px = 9 + -1q + qx + -1x Divide each side by 'x'. p = 9x-1 + -1qx-1 + q + -1 Simplifying p = 9x-1 + -1qx-1 + q + -1 Reorder the terms: p = -1 + q + -1qx-1 + 9x-1
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