One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Answer:

Since -3 is a root, identify x + 3 as a factor and use synthetic division to divide 2x^3 + 9x^2 + 7x - 6 by x + 3. The quotient is 2x^2 + 3x - 2 with remainder 0. Factoring the quotient gives (x + 2)(2x - 1), so the polynomial factors as (x + 3)(x + 2)(2x - 1).