Finding Zeros of Polynomials Flashcard

Front

What is the Fundamental Theorem of Algebra?

Back

The degree of the polynomial tells us how many solutions the polynomial will have.

Front

How do you find the zeros of a polynomial given one factor?

Back

If one factor is (x - a), then x = a is a zero of the polynomial.

Front

What are the zeros of the polynomial x^3 - 6x^2 + 11x - 6?

Back

x = 1, 2, 3.

Front

How do you find all zeros of a polynomial?

Back

Use factoring, synthetic division, or the quadratic formula to find all solutions.

Front

What is the conjugate root theorem?

Back

If a polynomial has real coefficients and a complex zero a + bi, then its conjugate a - bi is also a zero.

Front

Find the zeros of the polynomial f(x) = (x-5)(2x+3)(7x-4)(x+6).

Back

x = 5, -3/2, 4/7, -6.

Front

What is a rational zero?

Back

A rational zero is a solution of a polynomial equation that can be expressed as a fraction p/q, where p and q are integers.

Front

How do you apply the Rational Root Theorem?

Back

List all possible rational roots based on the factors of the constant term and the leading coefficient.

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear factor, simplifying the process of finding zeros.

Front

If a polynomial has a degree of 4, how many zeros can it have?

Back

It can have up to 4 zeros, counting multiplicities.