SOLUTION: How do you find all values of k so that {{{t^2+kt-8}}} can be factored using integers?

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Question 102122: How do you find all values of k so that t%5E2%2Bkt-8 can be factored using integers?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
How do you find all values of k so that t%5E2%2Bkt-8 can be factored using integers?
To factor
t%5E2%2Bkt-8=%28t%2Bu%29%2A%28t%2Bv%29
You must meet two conditions : the product of u and v must equal (-8) and the sum of u and v must equal k. The possible integer factors, without sign, of 8 are (1x8) and (2x4). The combinations, including the negatives and positives are then, (-1,8),(1,-8),(-2,4),(2,-4) since then products of all of these factors are (-8). The value for k is then the sum of these two factors or (7, -7, 2, -2)
or in equation form:
t%5E2%2B7t-8=%28t-1%29%2A%28t%2B8%29
t%5E2-7t-8=%28t%2B1%29%2A%28t-8%29
t%5E2%2B2t-8=%28t-2%29%2A%28t%2B4%29
t%5E2-2t-8=%28t%2B2%29%2A%28t-4%29