Fundamental Theorem of Algebra (Edited)

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n roots in the complex number system, counting multiplicities.

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

How many roots does a polynomial of degree 6 have?

Back

A polynomial of degree 6 has exactly 6 roots in the complex number system, which may include real and complex roots.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

Front

Solve: (8p^3 - 38p^2 - 17p + 43) ÷ (p - 5)

Back

8p^2 + 2p - 7, R 8

Front

Solve: (5p^2 + 5p - 26) ÷ (p + 3)

Back

5p - 10, R 4

Front

Solve: (4x^2 - 24x + 35) ÷ (2x - 5)

Back

2x - 7

Front

Solve: (27x^3 + 9x^2 - 3x - 10) ÷ (3x - 2)

Back

9x^2 + 9x + 5

Front

What is a real root?

Back

A real root of a polynomial is a solution to the polynomial equation that is a real number.

Front

What is a complex root?

Back

A complex root of a polynomial is a solution to the polynomial equation that is a complex number, which can be expressed in the form a + bi, where a and b are real numbers.