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
x^{4} + 7 x^{3}
-------------
3x^{3} + 25 x^{2}
3x^{3} + 21x^{2}
-------------------
4x^{2} + 15 x
4x^{2} + 28x
-----------------
-13x + K
- 13x - 91
----------------
K + 91
∴ K + 91 = 0
K= -91