The remainder when 3x^2 + 2x – 6 is divided by (2x – 1)
The remainder when 3x2 + 2x – 6 is divided by (2x – 1)
A) \(\frac{-37}{8}\)
B) \(\frac{-43}{8}\)
C) \(\frac{59}{3}\)
D) None
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Correct option is (D) None
Let p(x) = \(3x^2+2x-6\)
The remainder when p(x) is divided by \((2x-1)\) is \(p(\frac12).\)
Now, \(p(\frac12)=3(\frac12)^2+2\times\frac12-6\)
\(=\frac34+1-6=\frac34-5\)
\(=\frac{3-20}4=\frac{-17}4\)
Hence, when \((3x^2+2x-6)\) is divided by \((2x-1),\) it leaves remainder \(\frac{-17}4.\)
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