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, x + 3 is a factor. Use synthetic division with -3 and the coefficients 2, 9, 7, and -6. The quotient is 2x^2 + 3x - 2, with remainder 0. Factoring the quotient gives (x + 2)(2x - 1), so the factors of the polynomial are (x + 3)(x + 2)(2x - 1).