Solve the quadratic equation X^2+3X+2=0 by factorisation.

There are different ways of solving quadratic equations but this one asks for you to solve by factorisation. This is where you take the equation on the left hand side and rewrite it into brackets - two bits that times together to make the equation you started with. This will look like (Something)(Something)=0.

So you look at the bit that makes it complicated - the X^2, this is where you have two X's timesed together to make "X squared". So we start by putting one X in the first bracket and another in the other. Because X times X equals X^2 and that's the first bit we want. Now we move onto the next bit, this is a little complicated, but what we want is two numbers that times together to make 2 and add together to make 3. This may be clear to you straight away, but you can try different numbers to try and figure it out. The ones that are easiest to use are 1 and 2. 1x2=2 and 1+2=3. The reason we want to find this is because when we multiply out the brackets we want them to make the equation above.

This should look like (X+1)(X+2)=0. Lets double check the two brackets multiply out to make the equation we want. So you can use many ways of factoring out, one way is "the smiley face method" where you join lines from each part of the equation. So XxX=X^2, Xx2=2X, 1xX=X and 1x2=2, adding these all together makes X^2+2X+X+2=X^2+3X+2 which is what we wanted, so we factorised correctly.

Now we have the two brackets timesing each other, we can say that either the first one (X+1) equals zero, OR (X+2) equals zero, because if two things multiplied together makes zero, one of those things has to be equal to zero. So we put X+1=0 OR X+2=0. We solve the first one by taking away 1 from each side of the equals sign. X+1-1=0-1 which gives X=-1, so we have one possible answer. Then for the second one X+2=0, we take away 2 from either side, which gives X=-2. And there you have the answer: Either X=-1 OR X=-2.