**Factor Theorem**

If p(x)=(x-a)(x-b)…=0, then either x=a or x=b…

So each linear factor shows us a root (and conversely).

**Factor Theorem: p(t)=0 <=> x-t is a factor of p(x)**

When polynomials have small coefficients this can help us quickly find factors. We need only consider the divisors of the constant as any integer factor must divide it.

**Extended Factor Theorem: p(t/s)=0 <=> sx-t is a factor of p(x).**

**Worked Examples**

- 1.) Given that f(x) = x
^{3}– 6x^{2}+ 11x – 6,- Find f(0), f(1), f(2), f(3) and f(4);
- Factorise x
^{3}– 6x^{2}+ 11x – 6; - Solve the equation x
^{3}– 6x^{2}+ 11x – 6 = 0; - Sketch the curve whose equation is f(x) = x
^{3}– 6x^{2}+ 11x – 6

- 2.) Given that f(x) = x
^{3}– x^{2}– 3x + 2,- Show that x-2 is a factor;
- Solve the equation f(x) = 0.

**Exercise**

**Solutions**