Rational Root Theorem Practice

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that if a polynomial has rational roots, they can be expressed as the ratio of factors of the constant term and the leading coefficient.

Front

How do you find the possible rational zeros of a polynomial?

Back

To find possible rational zeros, list all factors of the constant term and the leading coefficient, then form all possible fractions of these factors.

Front

What are the possible rational zeros for the polynomial f(x) = x^3 + 2x^2 - 6x + 8?

Back

The possible rational zeros are ±1, ±2, ±4, ±8.

Front

Is (x-3) a factor of the polynomial f(x) = x^3 - 3x^2 + 2x + 2?

Back

No, (x-3) is not a factor.

Front

Which division method can be used for f(x) = x^4 + 3x^2 - 5 divided by (x + 7)?

Back

Synthetic division can be used.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

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 do you determine if a number is a zero of a polynomial?

Back

Substitute the number into the polynomial and check if the result is zero.

Front

What are the possible rational zeros for the polynomial f(x) = 3x^3 + 2x^2 - 6x + 7?

Back

The possible rational zeros are ±1, ±7, ±1/3, ±7/3.

Front

What is the significance of finding rational zeros in polynomials?

Back

Finding rational zeros helps in factoring the polynomial and solving equations.