Practice problem
Suppose b,c>0b,c > 0b,c>0 and x2+bx+cx^2+bx+cx2+bx+c can be factored. Must we be able to factor x2−bx+cx^2-bx+cx2−bx+c?
No. For example, b=5,c=4b=5, c=4b=5,c=4 is a counterexample!
No. Take b=2019b = 2019b=2019 and c=1c=1c=1 as a counterexample!
Yes. If x2+bx+c=(x+p)(x+q)x^2+bx+c = (x+p)(x+q)x2+bx+c=(x+p)(x+q) then x2−bx+c=(x−p)(x−q)x^2-bx+c = (x-p)(x-q)x2−bx+c=(x−p)(x−q).
Type a concept, like “slope” or “photosynthesis”.