Hello, Pinsky!

We are expected to be familiar with two theorems . . .Factor: .

Answer: . .

What is the procedure?

[1] The rational roots of a polynomial are of the form

. . .where is a factor of the constant term and is a factor of the leading coefficient.

Our polynomial has a constant term 10 with factors: .

. . and leading coefficient 1 with factors: .

Hence, the only possible rational roots are: .

[2] If , then is a factor of

We find that: .

. . Hence, is a factor.

Using long or synthetic division: .

. . And that quadratic factors: .

Therefore: .