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Simplifying 2x3 + -9x2 + -29x + -15 = (x2 + x + 3)(2x + m) Reorder the terms: -15 + -29x + -9x2 + 2x3 = (x2 + x + 3)(2x + m) Reorder the terms: -15 + -29x + -9x2 + 2x3 = (3 + x + x2)(2x + m) Reorder the terms: -15 + -29x + -9x2 + 2x3 = (3 + x + x2)(m + 2x) Multiply (3 + x + x2) * (m + 2x) -15 + -29x + -9x2 + 2x3 = (3(m + 2x) + x(m + 2x) + x2(m + 2x)) -15 + -29x + -9x2 + 2x3 = ((m * 3 + 2x * 3) + x(m + 2x) + x2(m + 2x)) -15 + -29x + -9x2 + 2x3 = ((3m + 6x) + x(m + 2x) + x2(m + 2x)) -15 + -29x + -9x2 + 2x3 = (3m + 6x + (m * x + 2x * x) + x2(m + 2x)) -15 + -29x + -9x2 + 2x3 = (3m + 6x + (mx + 2x2) + x2(m + 2x)) -15 + -29x + -9x2 + 2x3 = (3m + 6x + mx + 2x2 + (m * x2 + 2x * x2)) -15 + -29x + -9x2 + 2x3 = (3m + 6x + mx + 2x2 + (mx2 + 2x3)) Reorder the terms: -15 + -29x + -9x2 + 2x3 = (3m + mx + mx2 + 6x + 2x2 + 2x3) -15 + -29x + -9x2 + 2x3 = (3m + mx + mx2 + 6x + 2x2 + 2x3) Add '-2x3' to each side of the equation. -15 + -29x + -9x2 + 2x3 + -2x3 = 3m + mx + mx2 + 6x + 2x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -15 + -29x + -9x2 + 0 = 3m + mx + mx2 + 6x + 2x2 + 2x3 + -2x3 -15 + -29x + -9x2 = 3m + mx + mx2 + 6x + 2x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -15 + -29x + -9x2 = 3m + mx + mx2 + 6x + 2x2 + 0 -15 + -29x + -9x2 = 3m + mx + mx2 + 6x + 2x2 Solving -15 + -29x + -9x2 = 3m + mx + mx2 + 6x + 2x2 Solving for variable 'x'. Reorder the terms: -15 + -3m + -1mx + -1mx2 + -29x + -6x + -9x2 + -2x2 = 3m + mx + mx2 + 6x + 2x2 + -3m + -1mx + -1mx2 + -6x + -2x2 Combine like terms: -29x + -6x = -35x -15 + -3m + -1mx + -1mx2 + -35x + -9x2 + -2x2 = 3m + mx + mx2 + 6x + 2x2 + -3m + -1mx + -1mx2 + -6x + -2x2 Combine like terms: -9x2 + -2x2 = -11x2 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 3m + mx + mx2 + 6x + 2x2 + -3m + -1mx + -1mx2 + -6x + -2x2 Reorder the terms: -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 3m + -3m + mx + -1mx + mx2 + -1mx2 + 6x + -6x + 2x2 + -2x2 Combine like terms: 3m + -3m = 0 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 0 + mx + -1mx + mx2 + -1mx2 + 6x + -6x + 2x2 + -2x2 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = mx + -1mx + mx2 + -1mx2 + 6x + -6x + 2x2 + -2x2 Combine like terms: mx + -1mx = 0 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 0 + mx2 + -1mx2 + 6x + -6x + 2x2 + -2x2 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = mx2 + -1mx2 + 6x + -6x + 2x2 + -2x2 Combine like terms: mx2 + -1mx2 = 0 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 0 + 6x + -6x + 2x2 + -2x2 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 0 + 2x2 + -2x2 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -3m + -1mx + -1mx2 + -35x + -11x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 3m + mx + mx2 + 35x + 11x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 3m + mx + mx2 + 35x + 11x2)' equal to zero and attempt to solve: Simplifying 15 + 3m + mx + mx2 + 35x + 11x2 = 0 Solving 15 + 3m + mx + mx2 + 35x + 11x2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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