The Remainder Factor Theorem and Synthetic Division

Front

What is the Remainder Factor Theorem?

Back

The Remainder Factor Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c). This theorem helps in determining whether (x - c) is a factor of f(x).

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 divisor of the form (x - c). It is faster and requires less writing than long division.

Tags

CCSS.HSA.APR.D.6

Front

When using synthetic division, what do you do with the coefficients of the polynomial?

Back

You write down the coefficients of the polynomial in descending order of degree. If any degree is missing, use a coefficient of 0 for that degree.

Tags

CCSS.HSA.APR.D.6

Front

What does the remainder equal when a polynomial is divided by a factor?

Back

The remainder equals 0 when the polynomial is divided by a factor.

Tags

CCSS.HSA.APR.B.2

Front

How do you determine if (x - c) is a factor of f(x) using synthetic division?

Back

Perform synthetic division with c. If the remainder is 0, then (x - c) is a factor of f(x).

Tags

CCSS.HSA.APR.D.6

Front

What is the first step in synthetic division?

Back

The first step is to write down the coefficients of the polynomial in descending order.

Tags

CCSS.HSA.APR.D.6

Front

What is the significance of the remainder in synthetic division?

Back

The remainder indicates the value of the polynomial at the divisor's root. If the remainder is 0, it confirms that the divisor is a factor.

Tags

CCSS.HSA.APR.D.6

Front

How do you set up synthetic division for the polynomial f(x) = x^5 + 2x^4 + 9x^3 + 18x^2 + 40x + 77 divided by (x - 2)?

Back

Use the coefficients: 1, 2, 9, 18, 40, 77. The divisor is 2.

Tags

CCSS.HSA.APR.D.6

Front

What is the quotient when dividing f(x) = x^5 + 2x^4 + 9x^3 + 18x^2 + 40x + 77 by (x - 2)?

Back

The quotient is x^4 + 4x^3 + 17x^2 + 40x + 77.

Tags

CCSS.HSA.APR.D.6

Front

What is the formula for synthetic division?

Back

The formula for synthetic division is: 1. Write down the coefficients of the polynomial. 2. Bring down the leading coefficient. 3. Multiply and add down the column.

Tags

CCSS.HSA.APR.D.6