What is a factor of a polynomial?

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

Explain how to factor a quadratic trinomial of the form $$ax^2 + bx + c$$ .

To factor a quadratic trinomial, find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the trinomial and factor by grouping.

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

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

What does it mean for a polynomial to be in standard form?

A polynomial is in standard form when its terms are arranged in descending order of their degree.

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form $$x - c$$ .

What is the difference between a root and a factor of a polynomial?

A root of a polynomial is a value of $$x$$ that makes the polynomial equal to zero, while a factor is a polynomial that divides the original polynomial.

How do you determine if a polynomial is factorable over the integers?

A polynomial is factorable over the integers if its discriminant is a perfect square (for quadratics) or if it can be expressed as a product of polynomials with integer coefficients.

What is the purpose of the Factor Theorem?

The Factor Theorem states that a polynomial $$f(x)$$ has a factor $$x - c$$ if and only if $$f(c) = 0$$ .

Algebra 2 CA3 Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

Front

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k = 9

3.

FLASHCARD QUESTION

Front

Back

Remainder = 83

4.

FLASHCARD QUESTION

Front

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Remainder = -113

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Define a polynomial function.

Back

7.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

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