In the polynomial x^4 − 2x^3 + kx^2 + 3x + 1, k is a real number. For what value of k is ( x+1 ) a factor of the polynomial? The value of k is ___.

Since (x−2) is a factor of the polynomial 3x  

3

−2x  

2

+kx−6=0, we have

p(2)=0

i.e. 3(2)  

3

−2(2)  

2

+k(2)−6=0$

i.e. 24−8+2k−6=0

i.e. 2k=−10

i.e. k=−5.

Step-by-step explanation: