Since every polynomial of degree n has n roots, by the factor theorem it can be written (x-b)(x-a)... where a, b are roots of P(x)=0. So P(x) can be factored. What am I missing?
To factor , first solve it using the quadratic formula:
Of course, saying something can be done doesn't mean it will be easy! The quadratic formula fairly easily gives solutions to quadratic equations and so factors for quadratic polynomials. There are harder formulas for solutions to cubic and quartic polynomial equations. But there are polynomial equations of degree 5 and higher whose solutions cannot be written in terms of radicals and so while such polynomials can be factored, those factors cannot be written in any easy way.