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

Answer:

Identify the factor x + 3 from the given root –3. Use synthetic division to divide the polynomial by x + 3. Use the bottom row of the synthetic division as coefficients in the quadratic 2x2 + 3x – 2. Factor the quotient to find the two other factors: x + 2 and 2x – 1.