factorise the quadratic: v^2+20v+19

Recap defintions: factorise essentially means making the equation simpler by finding the common factors. 

This is a simple quadratic because the first term has a coeffecient of 1. therefore we know it will factorise into 2 brackets so we draw them out. (   )(   )

next we look at the first term, V^2. This means VxV so we put a V in each bracket so that when we mulitply the brackets it equals V^2.   (V   )(V    )

The next step is to find the factors of 19. Because this is a prime number the only factors are 1 and 19 and -1 and -19.

When we put this into the brackets and multiply the together we end up  V^2   +/- V  +/- V  +/- Number. This shows that the 2 factors that we chose need to add to make the second term in the equation, in this case 20.

We can use +1 and +19. so the answer is (V+1)(V+19). We then check this by mutliplying the brackets to together to see if we get the original equation.