The value of `k`, if `x^2+2x+k` is a factor of `2x^4+x^3-14x^2+5x+6` is

Explanation

To find the value of \( k \) such that \( x^2 + 2x + k \) is a factor of \( 2x^4 + x^3 - 14x^2 + 5x + 6 \), we will use polynomial long division. Here’s a step-by-step solution:

### Step 1: Set up the long division
We need to divide \( 2x^4 + x^3 - 14x^2 + 5x + 6 \) by \( x^2 + 2x + k \).

### Step 2: Divide the leading terms
The leading term of the dividend is \( 2x^4 \) and the leading term of the divisor is \( x^2 \). We divide these to find the first term of the quotient:
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