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).
