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Simplifying 2x3 + -10x2 + 11x + -7 = (x + -4)(2x2 + hx + 3) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = (x + -4)(2x2 + hx + 3) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = (-4 + x)(2x2 + hx + 3) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = (-4 + x)(3 + hx + 2x2) + k Multiply (-4 + x) * (3 + hx + 2x2) -7 + 11x + -10x2 + 2x3 = (-4(3 + hx + 2x2) + x(3 + hx + 2x2)) + k -7 + 11x + -10x2 + 2x3 = ((3 * -4 + hx * -4 + 2x2 * -4) + x(3 + hx + 2x2)) + k -7 + 11x + -10x2 + 2x3 = ((-12 + -4hx + -8x2) + x(3 + hx + 2x2)) + k -7 + 11x + -10x2 + 2x3 = (-12 + -4hx + -8x2 + (3 * x + hx * x + 2x2 * x)) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = (-12 + -4hx + -8x2 + (hx2 + 3x + 2x3)) + k -7 + 11x + -10x2 + 2x3 = (-12 + -4hx + -8x2 + (hx2 + 3x + 2x3)) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = (-12 + -4hx + hx2 + 3x + -8x2 + 2x3) + k -7 + 11x + -10x2 + 2x3 = (-12 + -4hx + hx2 + 3x + -8x2 + 2x3) + k Reorder the terms: -7 + 11x + -10x2 + 2x3 = -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 Add '-2x3' to each side of the equation. -7 + 11x + -10x2 + 2x3 + -2x3 = -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -7 + 11x + -10x2 + 0 = -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 + -2x3 -7 + 11x + -10x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -7 + 11x + -10x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 0 -7 + 11x + -10x2 = -12 + -4hx + hx2 + k + 3x + -8x2 Solving -7 + 11x + -10x2 = -12 + -4hx + hx2 + k + 3x + -8x2 Solving for variable 'x'. Reorder the terms: -7 + 12 + 4hx + -1hx2 + -1k + 11x + -3x + -10x2 + 8x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 12 + 4hx + -1hx2 + -1k + -3x + 8x2 Combine like terms: -7 + 12 = 5 5 + 4hx + -1hx2 + -1k + 11x + -3x + -10x2 + 8x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 12 + 4hx + -1hx2 + -1k + -3x + 8x2 Combine like terms: 11x + -3x = 8x 5 + 4hx + -1hx2 + -1k + 8x + -10x2 + 8x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 12 + 4hx + -1hx2 + -1k + -3x + 8x2 Combine like terms: -10x2 + 8x2 = -2x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = -12 + -4hx + hx2 + k + 3x + -8x2 + 12 + 4hx + -1hx2 + -1k + -3x + 8x2 Reorder the terms: 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = -12 + 12 + -4hx + 4hx + hx2 + -1hx2 + k + -1k + 3x + -3x + -8x2 + 8x2 Combine like terms: -12 + 12 = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 + -4hx + 4hx + hx2 + -1hx2 + k + -1k + 3x + -3x + -8x2 + 8x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = -4hx + 4hx + hx2 + -1hx2 + k + -1k + 3x + -3x + -8x2 + 8x2 Combine like terms: -4hx + 4hx = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 + hx2 + -1hx2 + k + -1k + 3x + -3x + -8x2 + 8x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = hx2 + -1hx2 + k + -1k + 3x + -3x + -8x2 + 8x2 Combine like terms: hx2 + -1hx2 = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 + k + -1k + 3x + -3x + -8x2 + 8x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = k + -1k + 3x + -3x + -8x2 + 8x2 Combine like terms: k + -1k = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 + 3x + -3x + -8x2 + 8x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 3x + -3x + -8x2 + 8x2 Combine like terms: 3x + -3x = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 + -8x2 + 8x2 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 5 + 4hx + -1hx2 + -1k + 8x + -2x2 = 0 The solution to this equation could not be determined.
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