How do I factorise a quadratic equation?
A quadratic equation will always take the form ax2 + bx + c, where x is a variable and a, b and c are numbers. The equation may be given to you with several x2 values, several x values or several numbers. Before beginning to solve the equation, make sure to write it in the form given above. The simplest method for solving a quadratic equation is what I like to call the 'Product, Sum, Number Method' or the 'PSN Method'. This can sound complicated when explained but it is very simple and easy to remember when practiced a few times! Write down the letters P, S and N below each other at the side of your page. Take the numbers represented by a and c in the quadratic equation and multiply them. Write this answer beside the letter P. Take the number represented by b in the quadratic equation and write it beside the letter S. Now find two numbers (positive or negative) which, when multiplied by each other equal the number beside P, and when added together equal the number beside S. Write these two numbers beside the letter N.Next, write the quadratic equation in the form ax2 + dx + ex + c, where d and e are the two numbers beside N. Factorise 'ax2 + dx' and then factorise 'ex + c'. You will be left with an equation in the form fx(g+x) + h(g+x). Writing this in the form (fx+h)(g+x) gives you the factorised version of the original quadratic equation!
