Question

Using remainder theorem show that (2x-3) is a factor of 2x³-9x²+x+12​

Answer 1

Step-by-step explanation:

Here is your answer..

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Answer 2

2x - 3 = 0

2x = 2

$x \: = \frac{3}{2}$

So, putting x as 3/2

$2 \times (\frac{3}{2}) {}^{3} - 9 \times (\frac{3}{2} ) {}^{2} + \frac{3}{2} + 12 \\ \frac{27}{4} - \frac{81}{4} + \frac{3}{2} + 12 \\ taking \: lcm \: \\ \frac{27 - 81 + 6 + 48}{4} \\ \frac{81 - 81}{4} \\ \frac{0}{4} \\ = 0$

As remainder is Zero... Hence (2x-3) is the factor

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