Factorise 8x^2 + 6x +1
8x2 + 6x + 1. This is a quadratic equation as the highest power of x is to the power of 2.A quadratic is written in the form: ax2 + bx + c. The coefficient of the x2 term is greater than one. So you need to find two numbers which add to get b and multiply to get ac. In the example shown above we need to find two numbers which add to get 6 and multiply to get 8. Can you think of two numbers? The numbers 4 and 2, add to 6 and multiply to get 8. Now write the equation like this: 8x2 + 4x + 2x + 1. It is still the same equation but it is now in a form where it can be easily factorised. Now split the equation into two halves and factorise these halves. 4x(2x + 1) + 1(2x + 1) What do you notice about this equation? (2x + 1) is a common factor. We can treat (2x + 1) in exactly the same way as we would treat x or any other algebraic variable. We can add 'like' terms. Like so: (4x + 1)(2x + 1). We have now factorised the quadratic.
