What is the Remainder Theorem?

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

What are complex roots?

Complex roots are solutions to polynomial equations that include imaginary numbers. They occur in conjugate pairs when the coefficients of the polynomial are real.

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

A polynomial of degree $$n$$ can have up to $$n$$ roots, counting multiplicities. This means that some roots may be repeated.

What is a zero of a polynomial?

A zero of a polynomial is a value of $$x$$ that makes the polynomial equal to zero. For example, if $$f(x) = x^2 - 4$$ , then the zeros are $$x = 2$$ and $$x = -2$$ .

How do you factor a quadratic polynomial?

To factor a quadratic polynomial of the form $$ax^2 + bx + c$$ , look for two numbers that multiply to $$ac$$ and add to $$b$$ . Then, rewrite the polynomial using these numbers.

What is the significance of the discriminant in quadratic equations?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of a quadratic equation. If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; and if $$D

What is the process of completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , which makes it easier to solve for $$x$$ .

Solve for the roots: $$x^3 + 4x^2 - 4x - 16 = 0$$

The roots are $$-4, \, \text{and} \, \text{±}2$$ .

Find all zeros for the polynomial $$P(x) = x^3 - 3x^2 - 5x + 15$$

The zeros are $$3, \, \text{±}√5$$ .

Solving polynomials by factoring Honors Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to factor a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

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