Is it possible to factor $3x^2+ 7x + 2$ ? If so, what are the factors?

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Answer 1 · 2016-02-28T13:50:59

$3x^2+7x+2" "=" " (3x+1)(x+2)$

The whole number factors of 3 can only be 1 and 3
The whole number factors of 2 can only be 1 and 2

$3xx2=6$ which is close to 7 so lets try it!

$color(blue)("Attempt 1")$

$(3x+2)(x+1) = 3x^2+3x+2x+2 =3x^2+color(red)(5x)+2 color(red)(" Fail"$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Attempt 2")$

$(3x+1)(x+2) = 3x^2+6x+x+2 =3x^2+7x+2 color(green)(" Works!")$

Is it possible to factor 3x^2+ 7x + 23x^2+ 7x + 2? If so, what are the factors?