x^3-4x^2-31x+70=(x-2)(ax^2+bx+c)

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Solution for x^3-4x^2-31x+70=(x-2)(ax^2+bx+c) equation: 


Simplifying
x3 + -4x2 + -31x + 70 = (x + -2)(ax2 + bx + c)

Reorder the terms:
70 + -31x + -4x2 + x3 = (x + -2)(ax2 + bx + c)

Reorder the terms:
70 + -31x + -4x2 + x3 = (-2 + x)(ax2 + bx + c)

Multiply (-2 + x) * (ax2 + bx + c)
70 + -31x + -4x2 + x3 = (-2(ax2 + bx + c) + x(ax2 + bx + c))
70 + -31x + -4x2 + x3 = ((ax2 * -2 + bx * -2 + c * -2) + x(ax2 + bx + c))
70 + -31x + -4x2 + x3 = ((-2ax2 + -2bx + -2c) + x(ax2 + bx + c))
70 + -31x + -4x2 + x3 = (-2ax2 + -2bx + -2c + (ax2 * x + bx * x + c * x))
70 + -31x + -4x2 + x3 = (-2ax2 + -2bx + -2c + (ax3 + bx2 + cx))

Reorder the terms:
70 + -31x + -4x2 + x3 = (-2ax2 + ax3 + -2bx + bx2 + -2c + cx)
70 + -31x + -4x2 + x3 = (-2ax2 + ax3 + -2bx + bx2 + -2c + cx)

Solving
70 + -31x + -4x2 + x3 = -2ax2 + ax3 + -2bx + bx2 + -2c + cx

Solving for variable 'x'.

Reorder the terms:
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = -2ax2 + ax3 + -2bx + bx2 + -2c + cx + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx

Reorder the terms:
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = -2ax2 + 2ax2 + ax3 + -1ax3 + -2bx + 2bx + bx2 + -1bx2 + -2c + 2c + cx + -1cx

Combine like terms: -2ax2 + 2ax2 = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0 + ax3 + -1ax3 + -2bx + 2bx + bx2 + -1bx2 + -2c + 2c + cx + -1cx
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = ax3 + -1ax3 + -2bx + 2bx + bx2 + -1bx2 + -2c + 2c + cx + -1cx

Combine like terms: ax3 + -1ax3 = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0 + -2bx + 2bx + bx2 + -1bx2 + -2c + 2c + cx + -1cx
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = -2bx + 2bx + bx2 + -1bx2 + -2c + 2c + cx + -1cx

Combine like terms: -2bx + 2bx = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0 + bx2 + -1bx2 + -2c + 2c + cx + -1cx
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = bx2 + -1bx2 + -2c + 2c + cx + -1cx

Combine like terms: bx2 + -1bx2 = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0 + -2c + 2c + cx + -1cx
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = -2c + 2c + cx + -1cx

Combine like terms: -2c + 2c = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0 + cx + -1cx
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = cx + -1cx

Combine like terms: cx + -1cx = 0
70 + 2ax2 + -1ax3 + 2bx + -1bx2 + 2c + -1cx + -31x + -4x2 + x3 = 0

The solution to this equation could not be determined.

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