Show all work to solve

3x^2 - 5x - 2 = 0

Factor and set each factor equal to zero.

x = 2, - 1/3

Explanation:

The first term is, 3x2 its coefficient is 3.

The middle term is, - 5x its coefficient is - 5.

The last term, "the constant", is - 2

Step-1 : Multiply the coefficient of the first term by the constant 3 • - 2 = - 6

Step-2 : Find two factors of - 6 whose sum equals the coefficient of the middle term, which is - 5.

-6 + 1 = - 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 1

3x2 - 6x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors:

3x • (x-2)

Add up the last 2 terms, pulling out common factors:

1 • (x-2)

Step-5 : Add up the four terms of step 4:

(3x+1) • (x-2)

Which is the desired factorization

Equation at the end of step 2:

(x - 2) • (3x + 1) = 0