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Question
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
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Solution
Let p(x) = 2x3 – 9x2 + x + 12
We have to show that, 2x – 3 is a factor of p(x).
i.e., `p(3/2) = 0`
Now, `p(3/2) = 2(3/2)^3 - 9(3/2)^2 + 3/2 + 12`
= `2 xx 27/8 - 9 xx 9/4 + 3/2 + 12`
= `27/4 - 81/4 + 3/2 + 12`
= `(27 - 81 + 6 + 48)/4`
= `(81 - 81)/4`
= 0
Hence, (2x – 3) is a factor of p(x).
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