Rational Roots Theorem

Front

What does the degree of a polynomial determine?

Back

The degree of the polynomial determines the maximum number of roots (real or complex) that the polynomial can have.

Front

What indicates that a binomial is a factor of a polynomial when using synthetic division?

Back

The remainder is zero.

Front

What is the Rational Roots Theorem?

Back

The Rational Roots Theorem states that any rational solution (or root) of a polynomial equation can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

List the possible rational zeros for f(x) = 3x^3 + 2x^2 - 6x + 7.

Back

±1, ±7, ±1/3, ±7/3.

Front

List the possible rational zeros for f(x) = x^3 + 2x^2 - 6x + 8.

Back

±1, ±2, ±4, ±8.

Front

What is a root of a polynomial?

Back

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

Front

How can you find the rational roots of a polynomial?

Back

By using the Rational Roots Theorem to list all possible rational roots and then testing them using synthetic division or substitution.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear binomial.

Front

What is the significance of a zero remainder in synthetic division?

Back

A zero remainder indicates that the binomial used in synthetic division is a factor of the polynomial.

Front

What are the factors of a polynomial?

Back

Factors of a polynomial are expressions that can be multiplied together to yield the original polynomial.