how do i factorise a quadratic equation when the coefficient of x^2 is not 1?
Let us take this quadratic equation as an example:2x2 - 3x - 14 = 0The key here is to look for two numbers that multiply to the same number that 2 and -14 multiply to make, so that is 28. The numbers should also add together to make -3.We can start by considering the factors of 28. There is 28 and 1, 7 and 4, 14 and 2.However, we want to make -28 so that means one of the factors must be positive and the other must be negative.In this case, it is -7 and 4 that we want to use, as they add up to- 3.So, now we split the 3x into -7x and 4x:2x2+ 4x -7x -14 = 0We now factorise it in two separate halves, like this:2x(x+ 2) - 7 (x+2) = 0The factors are the shared (x+2) bracket and the numbers before, so that is 2x - 7.So, the answer is (x+2)(2x-7) = 0
