The is a very simple question, but I have just started studying quadratics. I understand how to factor them using different methods and also understand solving a quadratic using the formula, but my question is why bother learning to factorise when the quadratic equation always allows you to solve a quadratic? Is there a point to factorising that I am missing? Thanks
[Math] Why not always use the quadratic equation
quadratics
Best Answer
If you are only interested in solving an equation like $$x^2+3x+2=0$$ you are of course free to use any method you like (completing the square, use any formula, try to factorize...). But there is more to that than just solving equations.
If you solve the equation above you will get $x_1=-2,x_2=-1$. The fact that based on these solutions you can now write $x^2+3x+2=(x-x_1)(x-x_2)=(x+2)(x+1)$ holds for polynomials with higher degree. So if you solved the equation $$x^3+6x^2+11x+6=0$$ (which is a little bit trickier and would likely involve long division of polynomials), you'd get $x_1=-3,x_2=-2,x_1=-3$ and hence could write $$x^3+6x^2+11x+6=(x+3)(x+2)(x+1).$$ Just to outline some uses:
So it is not just another method to solve a equation in yet another, maybe time saving way, but it actually has some relevance for more advanced problems.