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if the remainder on dividing the polynomials 2x ^4-kx^2+5x - 3k+3 by (x+2) is 4,then find the value of k. ​

Answer»

Question:

  • If the REMAINDER on dividing the polynomial 2x⁴ - kx² + 5X - 3k + 3 by ( x + 2 ) is 4, find the value of k.

Given:

  • p(x) = 2x⁴ - kx² + 5x - 3k + 3
  • Divisor = ( x + 2 )
  • Remainder = 4

To find:

  • The value of k.

Solution:

Here, p(x) = 2x⁴ - kx² + 5x - 3k + 3

Now, x + 2 = 0

=> x = (-2)

By using remainder theorem,

p(-2) = 2(-2)⁴ - k(-2)² + 5(-2) - 3k+ 3

= 32 - 4k - 10 - 3k + 3

= 32 - 10 + 3 - 3k - 4k

= 25 - 7k .......(I)

So here we GET the remainder as 25 - 7k.

But in the question it is given that remainder is 4, therefore both are equal.

So, 25 - 7k = 4

( Both are same remainder)

=> (-7k) = 4 - 25

=> (-7k) = (-21)

=> 7k = 21

( Negative signs got cancelled)

=> k = 21/7

=> k = 3

Answer:

  • Therefore the value of k is 3.


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