Advanced Factoring and Solving

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as the roots of the polynomial.

Front

How do you write a polynomial in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degree, with the highest degree term first.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

How do you find the roots of a factored polynomial?

Back

To find the roots of a factored polynomial, set each factor equal to zero and solve for x.

Front

What is a complex root?

Back

A complex root is a solution to a polynomial equation that includes imaginary numbers, typically in the form a + bi, where i is the imaginary unit.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

A polynomial of degree n will have exactly n roots, counting multiplicities and including complex roots.

Front

How do you determine the number of real roots of a polynomial?

Back

The number of real roots can be determined using the discriminant for quadratic polynomials or by analyzing the behavior of the polynomial graphically.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor, which is faster than long division.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).