SOLUTION: is 2x-3 a factor of 8x^3-27? Explain why or why not.

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Question 69230: is 2x-3 a factor of 8x^3-27? Explain why or why not.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
IN ORDER FOR (2X-3) TO BE A FACTOR OF (8X^3-27) WHEN DIVIED SHALL HAVE NO REMAINDER.
USING LONG DIVISION WE GET (8X^3-27)/(2X-3)=(4X^2+6X+9). THEREFORE (2X-3) IS A FACTOR OF (8X^3-27).
PROOF
WE MULTIPLY 4X^2+6X+9 BY 2X-3 THUS
------------------------------
4X^2+6X+9
*2X-3
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8X^3+12X^2+18X-12X^2-18X-27 OR
8X^3-27 THEREFORE
(2X-3)(4X^2+6X+9)=8X^3-27 AND (2X-3) IS A FACTOR.