Find all values of k so each trinomial can be factored using integers.

Question

3s^2 +ks - 14

Answer 1

3S + KS - 14.

A*C=3*-14 =-42 = -3*14 = -1*42 = 1*-42 = -2*21= 2*-21 = -6*7 = 6*-7.

K = 3 - 14 = -11.
Solve the Quad Eq and get:
S = 4 2/3, S = -1.
(S-4 2/3)(S+1) = 0,
(S-14/3)(S+1) = 0,
Multiply both terms inside the 1st pa-
renthesis by 3:
(3S-14)(S+1).

K = -3 + 14 = 11.
(S-1)(S+4 2/3) = 0,
(S-1)(3S+14) = 0.

K = -1 + 42 = 41
(S-1/3)(S+14) = 0,
(3S-1)(S+14) = 0.

K = 1 - 42 = -41.
(S-14)(S+1/3) = 0,
(S-14)(3S+1) = 0.

K = -2 + 21 = 19.
(X-2/3)(X+7) = 0,
(3X-2)(X+7) = 0.

K = 2-21 = -19.
(X-7)(X+2/3) = 0,
(X-7)(3X+2) = 0.

K = -6 + 7 = 1.
(X-2)(X+7/3) = 0,
(X-2)(3X+7) = 0.

K = 6 - 7 = -1.
(X-7/3)(X+2) = 0,
3X-7)(X+2) = 0.

Therefore,there are 8 values of k:
k = +-11, +-41, +-19, +-1.

Answer 2

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