Additional Mathematics – Factors of polynomials | e-Consult
Factors of polynomials (1 questions)
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Test possible integer roots (factors of the constant term \(-6\)): \(x=1\) gives \(1-6+11-6=0\). Hence \((x-1)\) is a factor.
Divide \(h(x)\) by \((x-1)\):
| \(x^{3}-6x^{2}+11x-6\) | ÷ | \(x-1\) |
| \(x^{2}-5x+6\) | ||
The quotient \(x^{2}-5x+6\) factors further: \(x^{2}-5x+6=(x-2)(x-3)\).
Thus the complete factorisation is
\[h(x)=(x-1)(x-2)(x-3).\]