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Factor the trinomial

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1 Answer

     3x2  +  17x  -  6

(a)

1.) determine the greatest common factor (gcf), if any:

     ==> since there is no common factor that divides into each term of the polynomial equally, there is no gcf

2.) set up a product of two binomials:

     ==>     (          )(          )

3.) find the first terms of the binomials:

     ==>   factors of   3x2 :     3x   and   x

     ==>     (3x        )(x         )

4.) find the second terms of the binomials:

     ==>   factors of   -6 :     -1 and 6 ,   1 and -6 ,   -2 and 3 ,   or   2 and -3

5.) use trial and error to determine which pair of factors make up the second two terms of the binomials:

     ==>     (3x  -  1)(x  +  6) = 3x2 + 18x - x - 6 = 3x2 + 17x - 6

     ==>     (3x  +  1)(x  -  6) = 3x2 - 18x + x - 6 = 3x2 - 17x - 6

     ==>     (3x  -  2)(x  +  3) = 3x2 + 9x - 2x - 6 = 3x2 + 7x - 6

     ==>     (3x  +  2)(x  -  3) = 3x2 - 9x + 2x - 6 = 3x2 - 7x - 6

Notice that the only pair of factors of -6 that yield the correct trinomial is the first, -1 and 6. Thus, the factored form of the original trinomial is:

     3x2 + 17x - 6 = (3x - 1)(x + 6)

(b) Since this polynomial is factorable it is not a prime polynomial.