Lab 20: Synthetic Division of Polynomials

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

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing down the coefficients of the polynomial and the zero of the divisor (c) on the left.

Tags

CCSS.HSA.APR.D.6

Front

How do you find the zero of the divisor in synthetic division?

Back

For a divisor of the form (x + a), the zero is -a. For (x - a), the zero is a.

Tags

CCSS.HSA.APR.D.6

Front

What do you do with the leading coefficient in synthetic division?

Back

Bring down the leading coefficient as the first number in the synthetic division process.

Tags

CCSS.HSA.APR.D.6

Front

What is the process of synthetic division after bringing down the leading coefficient?

Back

Multiply the zero of the divisor by the number just brought down, then add this result to the next coefficient.

Tags

CCSS.HSA.APR.D.6

Front

What does the final row of numbers represent in synthetic division?

Back

The final row represents the coefficients of the quotient polynomial, with the last number being the remainder.

Tags

CCSS.HSA.APR.D.6

Front

How do you express the result of synthetic division?

Back

The result is expressed as the quotient polynomial plus the remainder divided by the original divisor.

Tags

CCSS.HSA.APR.D.6

Front

What is the quotient when dividing (3x^3 - 2x^2 - 7x + 6) by (x + 1)?

Back

3x^2 - 5x - 2 + 8/(x + 1).

Tags

CCSS.HSA.APR.D.6

Front

What is the remainder when dividing (2x^3 - 5x^2 + 3x + 7) by (x - 2)?

Back

The remainder is 9.

Tags

CCSS.HSA.APR.B.2

Front

What is the result of dividing (x^3 - 3x^2 - 10x + 24) by (x + 3)?

Back

x^2 - 6x + 8.

Tags

CCSS.HSA.APR.D.6