Polynomial Division and Factorising Basics

Polynomial division works exactly like the long division you learned with numbers, except you're working with terms that have variables. The key is to divide the highest power terms first, then work your way down.

When dividing, always remember to change the signs when you subtract - this is where most mistakes happen! If you're subtracting a positive term, it becomes negative, and vice versa.

The examples show dividing expressions like $2x² + 5x + 11$ ÷ $2x + 4x - 3$. You set it up just like number division, with the dividend inside and divisor outside. Work term by term, starting with the highest powers.

Factorising is about finding the highest common factor first. For instance, 3x² - 9xy can be factored as 3x$x - 3y$ because 3x is the largest term that divides into both parts evenly.

Quick Tip: Always check your factorising by expanding it back out - if you get the original expression, you've done it right!