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Simplifying px2 + qx + r = (x + 1)(2x + -7) Reorder the terms: px2 + qx + r = (1 + x)(2x + -7) Reorder the terms: px2 + qx + r = (1 + x)(-7 + 2x) Multiply (1 + x) * (-7 + 2x) px2 + qx + r = (1(-7 + 2x) + x(-7 + 2x)) px2 + qx + r = ((-7 * 1 + 2x * 1) + x(-7 + 2x)) px2 + qx + r = ((-7 + 2x) + x(-7 + 2x)) px2 + qx + r = (-7 + 2x + (-7 * x + 2x * x)) px2 + qx + r = (-7 + 2x + (-7x + 2x2)) Combine like terms: 2x + -7x = -5x px2 + qx + r = (-7 + -5x + 2x2) Solving px2 + qx + r = -7 + -5x + 2x2 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1qx' to each side of the equation. px2 + qx + -1qx + r = -7 + -5x + -1qx + 2x2 Combine like terms: qx + -1qx = 0 px2 + 0 + r = -7 + -5x + -1qx + 2x2 px2 + r = -7 + -5x + -1qx + 2x2 Reorder the terms: px2 + r = -7 + -1qx + -5x + 2x2 Add '-1r' to each side of the equation. px2 + r + -1r = -7 + -1qx + -5x + -1r + 2x2 Combine like terms: r + -1r = 0 px2 + 0 = -7 + -1qx + -5x + -1r + 2x2 px2 = -7 + -1qx + -5x + -1r + 2x2 Reorder the terms: px2 = -7 + -1qx + -1r + -5x + 2x2 Divide each side by 'x2'. p = -7x-2 + -1qx-1 + -1rx-2 + -5x-1 + 2 Simplifying p = -7x-2 + -1qx-1 + -1rx-2 + -5x-1 + 2 Reorder the terms: p = 2 + -1qx-1 + -1rx-2 + -7x-2 + -5x-1
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