3x^2+17x-6

Select the correct choice below.

(a) 3x^2+17x-6=?

(b) The polynomial is prime.

3x^2+17x-6

Select the correct choice below.

(a) 3x^2+17x-6=?

(b) The polynomial is prime.

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3x^{2} + 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 3x^{2} : 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) = 3x^{2} + 18x - x - 6 = 3x^{2} + 17x - 6

==> (3x + 1)(x - 6) = 3x^{2} - 18x + x - 6 = 3x^{2} - 17x - 6

==> (3x - 2)(x + 3) = 3x^{2} + 9x - 2x - 6 = 3x^{2} + 7x - 6

==> (3x + 2)(x - 3) = 3x^{2} - 9x + 2x - 6 = 3x^{2} - 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:

3x^{2} + 17x - 6 = **(3x - 1)(x + 6)**

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

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