How do you find all zeros of a polynomial?

To find all zeros of a polynomial, factor the polynomial completely and set each factor equal to zero, then solve for $$x$$ .

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

A polynomial of degree $$n$$ can have at most $$n$$ real zeros, counting multiplicities.

What is the significance of the leading coefficient in a polynomial?

The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial's graph.

What is the difference between real and complex zeros?

Real zeros are the values of $$x$$ where the polynomial equals zero and are found on the real number line. Complex zeros are solutions that include imaginary numbers and do not correspond to points on the real number line.

What is the process of factoring a polynomial?

Factoring a polynomial involves rewriting it as a product of its factors. This can include finding common factors, using the difference of squares, or applying the quadratic formula.

What is the significance of the x-intercepts of a polynomial function?

The x-intercepts of a polynomial function are the points where the graph crosses the x-axis, corresponding to the real zeros of the polynomial.

How can you verify if a polynomial is a factor of another polynomial?

To verify if a polynomial $$g(x)$$ is a factor of another polynomial $$f(x)$$ , perform polynomial long division or synthetic division. If the remainder is zero, then $$g(x)$$ is a factor.

What is the role of the constant term in a polynomial?

The constant term of a polynomial is the value of the polynomial when $$x = 0$$ . It affects the vertical position of the graph.

Solving polynomials Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

4.

FLASHCARD QUESTION

Front

How do you find the remainder when dividing a polynomial by a linear factor?

Back

Tags

CCSS.HSA.APR.B.2

5.

FLASHCARD QUESTION

Front

What is a zero of a polynomial?

Back

Tags

CCSS.HSF-IF.C.7C

6.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

Tags

CCSS.HSA.APR.B.2

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