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What is 2x cubed plus x squared minus 13x plus 6 divided by x minus 2 giving reasons why your answer is correct?
Provided that x- 2 is not zero:
2x3 + x2 - 13x + 6 = 2x3 - 4x2 + 5x2 - 10x - 3x + 6
= 2x2*(x - 2) + 5x*(x - 2) - 3*(x - 2)
= (x - 2)*(2x2 + 5x - 3)
Therefore,
(2x3 + x2 - 13x + 6)/(x - 2) = (x - 2)*(2x2 + 5x - 3)/(x - 2) = 2x2 + 5x - 3
If x = 2 so that x - 2 = 0, then the expression is not defined.
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