Question

Help me find the value of k

Answer 1

• 
  `\tt k=3`

Explanation:

To solve this problem let's use the polynomial remainder theorem:-

For a polynomial p(x) and a number "a", the remainder on division by x - a is p(a).

According to the polynomial remainder theorem, the remainder when

P(x) is divided by (x+1), it can be rewritten as (x-(-1)), which equal to P(-1). We also know that the remainder is equal to 2, therefore we'll end up with P(-1)=2.

Now, let's use the above equality to find k:-

`\tt P(-1)=2`

`\tt 2(-1)^4-(-1)^3+2(-1)^2-k=2`

`\tt 2*1-(-1)+2*1-k=2`

`\tt 5-k=2`

`\tt k=3`

Therefore, k = 3.

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Hope this helps!