Factor the given polynomial.
3x² + 5x - 12

= ( x + 3 ) ( 3 x − 4 )

Step-by-step explanation:

Use a version of the AC Method.

A = 3 ,  B =5 ,  C = 12

Since the sign on the constant term is  − , look for a pair of factors of  A C = 36  whose difference is  B = 5

The pair  4 ,  9  works.

Now use that pair to split the middle term, then factor by grouping:

3 x 2 + 5 x − 12  = 3 x

− 4 x + 9 x − 12 = ( 3 x 2 − 4 x ) + ( 9 x − 12 )  = x                                                                              ( 3 x − 4 ) + 3 ( 3 x − 4 )

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