What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form $$x - c$$ . It is faster than long division for polynomials.

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. For example, a cubic polynomial can have up to 3 real zeros.

What is a quadratic polynomial?

A quadratic polynomial is a polynomial of degree 2, typically in the form $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants and @@a eq 0@@.

How do you factor a quadratic polynomial?

To factor a quadratic polynomial $$ax^2 + bx + c$$ , find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the polynomial using these numbers.

What is the difference between real and complex zeros?

Real zeros are the solutions to the polynomial that are real numbers, while complex zeros include imaginary numbers. For example, $$x^2 + 1 = 0$$ has complex zeros $$x = i$$ and $$x = -i$$ .

What is the significance 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's graph.

What is the importance 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; if D

Solving polynomials by factoring Flashcard

Student preview

15 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 are the zeros of a polynomial?

Back

Tags

CCSS.HSF-IF.C.7C

5.

FLASHCARD QUESTION

Front

How do you find the zeros of a polynomial by factoring?

Back

To find the zeros of a polynomial by factoring, first factor the polynomial into simpler polynomials, then set each factor equal to zero and solve for the variable.

Tags

CCSS.HSF-IF.C.7C

6.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

Tags

CCSS.HSA.APR.B.2

7.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

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