### Concept (1)

The rational roots theorem states that all potential roots are in the positive or negative form of the last coefficient s factors divided by the first coefficient s factors. With a large polynomial, solving by factoring is more difficult, and so finding the rational roots will give some potential zeros to start with. With these rational roots, the solutions after factoring complicated expressions is narrowed down to a select few answers.

### Sample Problems (4)

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Use the Rational Roots Theorem:

0 = 6x⁴ + 5x³ − 14x² + x + 2
###### Problem 1
How to find the rational roots of a polynomial.
###### Problem 2
Write a polynomial function with given real and imaginary roots.
###### Problem 3
The fundamental theorem of algebra, imaginary conjugates, and irrational conjugates as roots of a polynomial.
###### Problem 4
Listing all possible rational roots of a polynomial, then using synthetic division to find the zeros.