The Remainder Factor Theorem and Synthetic Division

Front

What is the Remainder Theorem?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

What is Synthetic Division?

Back

Synthetic Division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster and requires less writing than long division.

Tags

CCSS.HSA.APR.D.6

Front

How do you set up synthetic division?

Back

To set up synthetic division, write down the coefficients of the polynomial in descending order. If any degree is missing, use 0 as the coefficient for that degree.

Tags

CCSS.HSA.APR.D.6

Front

What is the first step in synthetic division?

Back

The first step in synthetic division is to write the value of c (from the divisor (x - c)) to the left and the coefficients of the polynomial to the right.

Tags

CCSS.HSA.APR.D.6

Front

What does the result of synthetic division represent?

Back

The result of synthetic division represents the coefficients of the quotient polynomial and the remainder.

Tags

CCSS.HSA.APR.D.6

Front

How do you find the quotient using synthetic division?

Back

To find the quotient using synthetic division, perform the synthetic division process and the resulting coefficients represent the polynomial quotient.

Tags

CCSS.HSA.APR.D.6

Front

What is the significance of the remainder in synthetic division?

Back

The remainder in synthetic division indicates the value of the polynomial at the divisor's root. If the remainder is 0, it means (x - c) is a factor of the polynomial.

Tags

CCSS.HSA.APR.D.6

Front

What is the relationship between the Remainder Theorem and synthetic division?

Back

The Remainder Theorem can be verified using synthetic division; the remainder obtained from synthetic division is equal to f(c), confirming the theorem.

Tags

CCSS.HSA.APR.B.2

Front

How do you handle missing degrees in synthetic division?

Back

When handling missing degrees in synthetic division, include a 0 as the coefficient for any missing degree to maintain the correct structure.

Tags

CCSS.HSA.APR.D.6

Front

What is the formula for the Remainder Theorem?

Back

The formula for the Remainder Theorem is: If f(x) is a polynomial and c is a constant, then the remainder of f(x) divided by (x - c) is f(c).

Tags

CCSS.HSA.APR.B.2