Explain polynomials, Mathematics

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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

2307_divide.png

           x4 + 7 x3

          -------------

           3x3 + 25 x2

           3x3 + 21x2

         -------------------

           4x2 + 15 x

           4x2 + 28x

           -----------------

            -13x + K

           - 13x - 91

             ----------------

               K + 91

∴ K + 91 = 0

K= -91


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