Factorise x^2 - 8x + 12

First we need to draw our two brackets where the terms will go, we set them out like so ( )( ). Now looking at the coefficient of the x squared term, we se that it is one, therefore, it is formed by a multiplication of x by x. We can now write an x at the start of each bracket, so we now have (x )(x ). We now need to look at our next two terms, we know that two numbers have to multiply together to give us 12, and add to give us 8. Thinking about the possible factors of 12, it is either 1 and 12, 3 and 4, or 6 and 2. The only set there that add to 8 is 6 and 2, therefore we know that they will be in our brackets as well. However, before we put them in, we need to remember back to the question that it is negative 8x, therefore the 6 and 2 add to a negative 8. This means that they must be negative 6 and negative 2. We know this gives us our -8x, and we check that multiplying the negative 2 and negative 6 gives us 12, 2 multiplied by 6 = 12, and a negative multiplied by a negative equals a positive. Therefore we know the answer must be correct. Can we now finish off our brackets, and write out the answer, (x - 6)(x - 2).