We have the Rational Roots Theorem.Solve algebraically: .
If a polynomial has a rational root, it is of the form
. . where is a factor of the constant term
. . and is a factor of the leading coefficient.
The constant term is with factors: .
The leading coefficient is with factors: .
That's a lot of fractions to test, but we may get lucky . . .
Try . . . no
Try . . . YES!
Since is a zero of , then is a factor.
Using long division, we have: .
. . And we find that the quadratic also factors.