Question

3x^2+5x+2 factor the expression

Answer 1

Answer:

Step-by-step explanation:

One factor must end in 2 and the other in 1, so as to get the constant term +2 of the given expression.  Possible roots are plus or minus 1, 2, 1/3 (for starts).

Use synthetic division to determine whether a possible root actually is a root.  If we choose to check out 1/3 as a possible root, we'd use:

1/3    /     3     5     2

                      1     2

      ----------------------

              3       6    4  Since the remainder is not zero, 1/3 is not a root.

Apply the quadratic formula.  Here a  = 3, b = 5 and c = 2, so the discriminant is b^2 - 4ac, or 25 - 4(3)(2) = 25 - 24 = 1, and the roots are

      -5 ± √1

x = ------------- = -6/6 (or -1) and -4/6 = -2/3

            6

Back to synthetic division:

-2/3   /     3    5    2

                     -2   -2

               -------------------

                3    3      0  (Remainder is zero).

Since -2/3 is a root, (3x + 2) is a factor.  The coefficients of the quotient

(found immediately above) are 3  3, indicating a factor of 3(x + 1).