Factorise the Quadratic: 3x^2 + 2x - 1.
When we are asked to factorise a quadratic we essentially need to tidy it up by putting it into brackets.For a quadratic we look to work out the sum and the product, however this time it's a bit different as we have coefficient of 3x2. This means we need to find the common factors of the coefficient (3) and the product (-1). 3 is a prime number therefore conveniently the only possible factors are 1 and 3. It should also be noted that we have a negative product and so one of the factors must be negative.In order to get our sum of 2x from our factors we can subtract 1 from 3 as 3 - 1 = 2. This means 1 is our negative factor. Written out you should now have 3x2 - x + 3x -1. (Notice how the quadratic is still the same only written in a slightly different format.)When we factorise this we can simply take out x for our first brackets so 3x2- x becomes x(3x - 1).And for the second bracket we just take out 1 so 3x - 1 becomes 1(3x-1).We know we've factorised correctly when the two brackets are the same: x(3x - 1) + 1 (3x - 1)We can now write out the factorised quadratic and our answer as: (x + 1)(3x - 1).This is a much tidier way of writing the same quadratic as we began with.
