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POLYNOMIALS: It is not once nor twice but times without number that the same ideas make their appearance in the world.
1. Find the value for K for which x4 + 10x3 + 25x2 + 15x + K exactly divisible by x + 7.
Ans: Let P(x) = x4 + 10x4 + 25x2 + 15x + K and g(x) = x + 7
Since P(x) exactly divisible by g(x)
∴ r (x) = 0
(Ans : K= - 91)
now
x4 + 7 x3
-------------
3x3 + 25 x2
3x3 + 21x2
-------------------
4x2 + 15 x
4x2 + 28x
-----------------
-13x + K
- 13x - 91
----------------
K + 91
∴ K + 91 = 0
K= -91
Submit your working in (neat) handwritten form (do not type up your solutions). For the plots that you generate in Maple or Matlab, you can print them out and attach them at the en
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