Additional Mathematics – Factors of polynomials | e-Consult

Answer 1

1. Test possible integer roots using the Rational Root Theorem. The constant term is \(-6\); possible roots are \(\pm1,\pm2,\pm3,\pm6\).
2. Evaluate \(f(1)=1-6+11-6=0\). Hence, \((x-1)\) is a factor.
3. Perform synthetic division of \(f(x)\) by \((x-1)\):

The quotient is \(x^{2}-5x+6\).

4. Factor the quadratic: \(x^{2}-5x+6=(x-2)(x-3)\).
5. Combine all factors: \(\boxed{f(x)=(x-1)(x-2)(x-3)}\).