Since this is SAT, substitute all the options and get the answer. -1 must be a root of x^2 + kx + 7.

(a) x^2 + 7, -1 is not a root

(b) x^2 + x + 7, -1 is not a root

(c) x^2 + 7x + 7, -1 is not a root

(d) x^2 + 8x + 7, -1a rootis

So (d) is the answer.

Direct method is to compare (x+1)(x+h) with x^2 + kx+7.

x^2 + (h+1)x + h = x^2 + kx + 7.

So h+1 = k and h = 7;

Thus k = 7+1 = 8;

(a) is not the answer. if k is 2, then 2k is not "twice the value of an odd integer"

However 2k+1 is always odd and therefore 2(2k+1) = 4k+2 is "twice the value of an odd integer". So (e) is correct