Perform synthetic division for $$2x^3 - 5x^2 - 4x - 25$$ by $$x - 4$$ .

The result is $$2x^2 + 3x + 8 + \frac{-57}{x - 4}$$ .

How do you apply the Remainder Theorem to find the remainder of $$3x^3 - 5x^2 - 4x + 1$$ divided by $$x + 3$$ ?

Evaluate the polynomial at $$x = -3$$ : $$3(-3)^3 - 5(-3)^2 - 4(-3) + 1 = -113$$ .

What is the relationship between the degree of a polynomial and its division?

When dividing a polynomial of degree $$n$$ by a polynomial of degree $$m$$ , the result will be a polynomial of degree $$n - m$$ .

What is the formula for polynomial long division?

The formula 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.

What is the first step in polynomial long division?

Identify the leading term of both the dividend and the divisor.

What does it mean if the remainder is zero in polynomial division?

If the remainder is zero, it means that the divisor is a factor of the dividend.

How do you check your work after performing polynomial division?

Multiply the quotient by the divisor and add the remainder; the result should equal the original polynomial.

What is the purpose of polynomial division in algebra?

Polynomial division is used to simplify expressions, find roots, and analyze polynomial functions.

What is the result of dividing $$x^2 + 3x + 2$$ by $$x + 1$$ ?

The result is $$x + 2$$ with a remainder of $$0$$ .

What is the definition of a polynomial?

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

Alg 2 Module 3 Test Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

2.

FLASHCARD QUESTION

Front

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

Back

3.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the significance of the remainder in polynomial division?

Back

The remainder indicates what is left over after division; it can provide insights into the roots of the polynomial.

7.

FLASHCARD QUESTION

Front

Back

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