Hello, Mike!

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 aof fractions to test, but we may get lucky . . .lot

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.

Therefore: .