Question 93733
Find two integers c (positive or negative) for which each polynomial can be factored.
x^2+x+c
The coefficient of the middle term is "1".
You need to think of two numbers whose sum is "1"
Like: +2 and -1 whose product is -2
Like: +3 and -2  whose product is -6
Like: +4 and -3 whose product is -12
etc.
c could now be -2 or -6 or -12 etc.
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Try some of these and see that you do get a factorable trinomial.
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x^2-2x+c
The coefficient of the middle term is "-2"
You need to think of two number whose sum is -2
like -3 and 1 whose product is -3
Like -4 and 2 whose product is -8
etc.
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x^2-3x+c
Like -4 and 1 whose product is -----
Like -5 and 2 whose product is ....

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Cheers,
Stan H.