Give the possible values of x when x^2 - 5x + 4 = 0
First, when faced with a question like this you must factorise the expression. So we need to factorise x2-5x+4 into 2 linear parts. (Linear terms are terms without any powers of x). To do this, we need to find 2 numbers that add together to make -5 and times together to give 4. The only numbers that have both of these properties are -4 and -1.So we have (x-4)(x-1)= x2-5x+4. To check this we can expand out the brackets.We now need to solve (x-4)(x-1)=0 to solve our original question. As we know, anything multiplied by 0 gives 0, therefore (x-4)=0 and (x-1)=0 are two solutions to the problem, therefore x=4 or x=1 by rearranging.
