SOLUTION: Find all positive values of k so that the trinomial can be factored. Show the factorization for each value of k you find. 3x^2 + kx

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Question 1164615: Find all positive values of k so that the trinomial can be factored. Show the factorization for each value of k you find.
3x^2 + kx - 15
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The factorization is of the form

(ax+b)(cx+d)

We know

(1) ac=3
(2) bd=-15

We can assume a and c are positive, because having both negative will not lead to different factorizations.

List all the possible factorizations that satisfy (1) and (2) and identify the ones that have k>0.

(3x+1)(x-15) k = -44
(3x-1)(x+15) k = 44
(3x+3)(x-5) k = -12
(3x-3)(x+5) k = 12
(3x+5)(x-3) k = -4
(3x-5)(x+3) k = 4
(3x+15)(x-1) k = 12
(3x-15)(x+1) k = -12

ANSWER: The possible positive values of k for which the trinomial can be factored are 4, 12, and 44

SOLUTION: Find all positive values of k so that the trinomial can be factored. Show the factorization for each value of k you find. 3x^2 + kx - 15