Question

find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6
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Answer 1

Use long division method :

After this

We got 2 equation

Equation 1 is 21+7k = 0

So let's solve it

7k = -21

k= -21/7 = -3

AND

Equation 2 is 2k²+8k+6 = 0

Let's solve this to find the actual value of k

2k²+8k+6 = 0 (by mid term splitting)

2k²+2k+6k +6 =0

2k( k+1) + 6(k+1)

( 2k+6) (k+1)

2k+6 = 0

k= -3

and k = -1

But in equation 1 we got k = -3 and equation 2 also we got k=-3

So, k=-3 is the correct answer.

Hope it helps you