What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

How do you solve a quadratic equation by factoring?

To solve by factoring, express the quadratic in the form $$(x - p)(x - q) = 0$$ , then set each factor to zero: $$x - p = 0$$ and $$x - q = 0$$ .

What is a polynomial function?

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

What does it mean for a polynomial to be factored completely?

A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system (e.g., real or complex numbers).

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

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

How do you identify the zeros of a polynomial function?

To identify the zeros, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

What is the Fundamental Theorem of Algebra?

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

What is the process of long division for polynomials?

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by that result, and subtracting from the dividend, repeating until the remainder is of lower degree.

Factoring and Finding Polynomial Zeros Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What are polynomial zeros?

Back

Polynomial zeros are the values of x that make the polynomial equal to zero. They are also known as roots or solutions of the polynomial.

Tags

CCSS.HSF-IF.C.7C

3.

FLASHCARD QUESTION

Front

How do you find rational zeros of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

5.

FLASHCARD QUESTION

Front

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

Back

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

6.

FLASHCARD QUESTION

Front

How do you factor a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring techniques such as difference of squares or the quadratic formula.

7.

FLASHCARD QUESTION

Front

What is the difference of squares?

Back

Tags

CCSS.HSA.APR.C.4

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