If (f(x) = 6x^{3} + 13x^{2} + 2x – 5) and (f(-1) = 0), find the factors of f(x).
Explanation
(f(x) = 6x^{3} + 13x^{2} + 2x – 5)
f(-1) = 0 implies (x + 1) is a factor.
Using the method of long division, you find the other factors.
(frac{6x^{3} + 13x^{2} + 2x – 5}{x + 1} = 6x^{2} + 7x – 5) (check).
(6x^{2} + 7x – 5 = 6x^{2} – 3x + 10x – 5)
(3x(2x – 1) + 5(2x – 1))
Hence, the factors of f(x) are (x + 1), (3x + 5) and (2x – 1).