For what values of b is the expression $x^2+bx+12$ factorable?

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Answer 1 · 2016-10-26T12:01:57

$+-13, +-8, +-7$
These are the possible sums of the factor pairs of 12

b is the sum of the factors used to multiply to get 12 for the C value.

$( x + 1) xx (x + 12) = x^2 + 13 x + 12$
$( x - 1) xx (x - 12) = x^2 + (-13) x + 12$

$(x + 2) xx (x + 6) = x^2 + 8x + 12$
$(x - 2) xx (x - 6) = x^2 + (-8)x + 12$

$(x + 3) xx ( x+ 4) = x^2 + 7 x + 12$
$(x - 3) xx ( x -4) = x^2 + (-7) x + 12$

These are the only whole number factors of 12 which can be factored.

For what values of b is the expression x^2+bx+12x^2+bx+12 factorable?