I’m doing partial fractions and need to factorize the denominator. They are quadratic. However there are some that aren’t so easy to factorize and my first choice was to use the quadratic equation to find the roots however comparing my answer with the correct one the signs are different. Is the quadratic formula only to be used when the equation is equal to zero? The answer used another method of factorizing that didn’t involve equating anything to zero and I can’t find anything about it online. Where did I go wrong? My denominator is:
the correct answer is: $-(3z+1)(z+1)$
while if I do this using the quadratic formula I get: $(3z+1)(z+1)$
however if I factorize the negative sign then use the quadratic formula I get the correct answer which is confusing to me.