Rational Root Theorem

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you determine possible rational roots using the Rational Root Theorem?

Back

To find possible rational roots, list all factors of the constant term (p) and all factors of the leading coefficient (q). The possible rational roots are then the combinations of these factors in the form p/q.

Front

What are the possible rational roots for the polynomial f(x) = 2x^3 + 5x^2 - 9x + 5?

Back

The possible rational roots are ±1, 5, 1/2, and 5/2.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

How can you verify if a number is a root of a polynomial?

Back

To verify if a number is a root, substitute it into the polynomial equation. If the result is zero, then it is a root.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c). It is used to find polynomial roots more efficiently.

Front

What is the significance of finding rational roots in polynomial equations?

Back

Finding rational roots helps in factoring the polynomial, which can simplify solving the equation and finding other roots.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What is the constant term in a polynomial?

Back

The constant term is the term in a polynomial that does not contain any variables, representing the value of the polynomial when all variable terms are zero.

Front

How do you factor a polynomial once a root is found?

Back

Once a root is found, you can use synthetic division to divide the polynomial by (x - root), resulting in a lower-degree polynomial that can be factored further.