The expression \( 2x^{3}\)+\(x^{2} \)-\(2x \)-\( 1\)divisible by
Correct Answer: Description for Correct answer:
From option (a)
x + 2 = 0 = > x = - 2
For x = -2, \( \Large 2x^{2} + x^{2} - 2x - 1 \)
\( \Large 2(-6)^{3} + (-2)^{2} - 2(-2) - 1 \)
= -16 + 4 + 4 - 1
= 8 - 17
\( \Large = -9 \ne 0 \)
Hence \( \Large 2x^{3} + x^{2} - 2x - 1 \) is not divisible x + 2
From option (b)
2x + 1 = 0 = > x = -1/2,
For x = -1/2
\( \Large 2x^{3} + x^{2} - 2x - 1 \)
\( \Large 2 \left( - \frac{1}{2}\right)^{3} + \left( - \frac{1}{2}\right)^{2} - = 2\left( - \frac{1}{2}\right) - 1 \)
= \( \Large = - \frac{2}{8} + \frac{1}{4} + 1 - 1\)
\( \Large = - \frac{1}{4} + \frac{1}{4} + 0 = 0 \)
Hence \( \Large 3x^{3} + x^{2} - 2x - 1 \) is divisible by 2x + 1
Hence option (b)is correct.
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