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Question
Show that x + 3 is a factor of 69 + 11x – x2 + x3.
Solution
Let p(x) = x3 – x2 + 11x + 69
We have to show that, x + 3 is a factor of p(x).
i.e., p(–3) = 0
Now, p(–3) = (–3)3 – (–3)2 + 11(–3) + 69
= –27 – 9 – 33 + 69
= – 69 + 69
= 0
Hence, (x + 3) is a factor of p(x).
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