Polynomial basic 2024_25

Front

What is the Conjugate Root Theorem?

Back

The Conjugate Root Theorem states that if a polynomial has real coefficients and a complex root (a + bi), then its conjugate (a - bi) is also a root.

Front

Given a complex zero 7-5i, what is the other zero according to the Conjugate Root Theorem?

Back

7+5i

Front

What is the conjugate of the complex number -3 + (4/5)i?

Back

-3 - (4/5)i

Front

How do you write a polynomial in factored form using its roots?

Back

If the roots are r1, r2, ..., rn, the polynomial can be expressed as (x - r1)(x - r2)...(x - rn).

Front

Write the factored form of a polynomial with roots 7 and -2i.

Back

(x-7)(x+2i)(x-2i)

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial of lower degree that divides the original polynomial without leaving a remainder.

Front

How can you determine if (x-3) is a factor of 3x^3 + 10x^2 - x - 12?

Back

Use polynomial long division or synthetic division to check if the remainder is zero.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem provides a list of possible rational roots of a polynomial based on the factors of the constant term and the leading coefficient.

Front

If a polynomial has a leading coefficient of 3 and a constant term of -12, what are the possible rational roots?

Back

The possible rational roots are the factors of -12 divided by the factors of 3.

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.