## Factorising Cubics

Factorising quadratic expressions is comparatively easy. If the coefficient of is one you can often find the factors by inspection. For example, to factorise find 2 numbers that add or take away to give 3 and multiply to give 18. By inspection we obtain 6 and 3. Then we can factorise: When we try and factorise a cubic we can start by finding common factors. This may reduce the problem to one of factorising a quadratic: The expression inside the brackets now factorises by inspection: find two numbers that add or take away to give -5 and multiply to give 6. We obtain -2 and -3. Hence, If we can't reduce the problem to factorising a quadratic by inspection, then things get a little more involved. Consider how to factorise a quadratic where the coefficient of is not one. For example, Multiply the coefficient of 2 by the constant term, 5 to get 10. Now look for the two factors of 10 that add to give the coefficient of 7. The two factors are 2 and 5. Now Example: Factorise the cubic expression Factorise first with the common factor 3x to give To factorise the quadratic in the brackets, multiply the coefficient of 2 by the constant term, 7 to get 14, then find the factors of 14 that add to give 9. The answer is 2 and 7. Hence hence the cubic factorises as Example: Factorise the cubic expression Factorise first with the common factor 2x to give To factorise the quadratic in the brackets, multiply the coefficient of 2 by the constant term, 9 to get 18, then find the factors of 18 that add to give 9. The answer is 3 and 6. Hence hence the cubic factorises as  