For a polynomial P and a 0: ax+b is a factor of P(x) P!(- ba)=0 If r!= s, then (x-r)(x-s) is a factor exactly when P(r)=P(s)=0. For a repeated factor, testing the root once is insufficient; divide again to check the required multiplicity.

\(ax+b\text{ is a factor of }\mathrm{P}(x)\quad\Longleftrightarrow\quad \mathrm{P}\!\left(-\dfrac ba\right)=0\)

If \(r\ne s\), then \((x-r)(x-s)\) is a factor exactly when \(\mathrm{P}(r)=\mathrm{P}(s)=0\).

For a repeated factor, testing the root once is insufficient; divide again to check the required multiplicity.

Factor Theorems

Factor Theorems

Video Solution:

Solution:

Solution locked