What is the result of dividing $$2x^8 - 8x^2 - 28x$$ by $$2x$$ ?

The result is $$x^7 - 4x - 14$$ .

What is the Remainder Theorem?

The Remainder Theorem states that the remainder of the division of a polynomial $$f(x)$$ by $$x - c$$ is equal to $$f(c)$$ .

If dividing $$x^6 + 4x^3 + 2$$ using synthetic division, how many zeros are needed in the top row?

You need 4 zeros in the top row.

What is the quotient when $$8b^3 - 17b^2 - b + 2$$ is divided by $$b - 2$$ ?

The quotient is $$8b^2 - b - 3$$ .

What is the first step in long division of polynomials?

The first step is to divide the leading term of the dividend by the leading term of the divisor.

What happens if the degree of the dividend is less than the degree of the divisor?

If the degree of the dividend is less than the degree of the divisor, the quotient is 0 and the dividend is the remainder.

What is the significance of the coefficients in synthetic division?

The coefficients represent the terms of the polynomial, and they are used to perform the synthetic division process.

How can you check your work after performing polynomial division?

You can check your work by multiplying the quotient by the divisor and adding the remainder; the result should equal the original polynomial.

Polynomial Division: 2 methods Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial or a monomial, similar to long division with numbers.

Tags

CCSS.HSA.APR.D.6

2.

FLASHCARD QUESTION

Front

What are the two main methods of polynomial division?

Back

The two main methods of polynomial division are long division and synthetic division.

Tags

CCSS.HSA.APR.D.6

3.

FLASHCARD QUESTION

Front

How do you divide a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

Tags

CCSS.HSA.APR.D.6

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

5.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

6.

FLASHCARD QUESTION

Front

How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial and the zero of the divisor (c) on the left.

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

What is the purpose of the remainder in polynomial division?

Back

The remainder represents what is left over after dividing the polynomial, and it can be expressed as a fraction of the divisor.

Tags

CCSS.HSA.APR.B.2

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