Question

If p(x)=x^787-x^786+k is divided by (x+1) then k=________.

Answer 1

Question: If p(x) = x^787-x^786+k is divisible by (x+1), then k=_______.

(Slightly Corrected)

• The factor theorem states,

    A polynomial p(x) has a factor (x - k) if and only if p(k)=0

   (i.e. k is a root).

• Since the polynomial p(x) is divisible by (x+1) or (x-(-1)), it implies:

                                       p(-1)=0

• So, putting x  = -1 in p(x), we get:

                         p(-1) = (-1)⁷⁸⁷-(-1)⁷⁸⁶+k = 0

             or,        (-1) - (+1) + k =0

             or,        k = 2

• Hence the result is :

                          k = 2

Answer 2

The value of k is equal to 2.

Step-by-step explanation:

Given,

The poynomial $p(x)=x^{787}-x^{786}+k$           ...... (1)

To find, the value of k = ?

∵ x + 1 = 0

⇒ x = - 1

Put x = - 1 in equation (1), we get

p( - 1) = 0

$(-1)^{787}-(-1)^{786}+k = 0$

⇒ - 1 - 1 + k = 0

⇒ k - 2 = 0

⇒ k = 2

∴ The value of k = 2

Thus, the value of k is equal to 2.