If \(f(x) = 6x^{3} + 13x^{2} + 2x - 5\) and \(f(-1) = 0\), find
FURTHER MATHEMATICS
WAEC 2011
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).
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