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Let p(x) be a cubic
polynomial such that
(p(x))2 + (x4 + 2x2 + 2x)2 = f(x) = (x2+1)(x2+4)(x2-
2x+2)(x2+2x+2). Find the value of |p(-3)|.
Answer.
Put f(-3)
(p(-3))2 + ((-3)4 + 2(-3)2 + 2(-3))2 = f(-3) = ((-3)2+1)
((-3)2+4)((-3)2-2(-3)+2)((-3)2+2(-3)+2)
(p(-3))2 + (81 + 18 - 6)2 = (9+1)(9+4)(9 + 6 +2)(9 – 6
+ 2)
(p(-3))2 + 8649 =
(10)(13)(17)(5)
(p(-3))2 = 11050 –
8649
(p(-3))2 = 2401
p(-3) = ± 49
We have to find |p(-3)| . So, |± 49| = 49 = |p(-3)|
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