Synthetic Division

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 than long division and focuses on the coefficients of the polynomial.

Tags

CCSS.HSA.APR.D.6

Front

How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial in descending order. If any degree is missing, use a zero as a placeholder. Place the value of c (from x - c) to the left.

Tags

CCSS.HSA.APR.D.6

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

A zero placeholder is used to maintain the correct degree of the polynomial when a term is missing. It ensures that the synthetic division process accurately reflects the polynomial's structure.

Tags

CCSS.HSA.APR.D.6

Front

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

Back

The result is (x - 4)(x - 2).

Tags

CCSS.HSA.APR.B.2

Front

What are the coefficients obtained after performing synthetic division on (3x - 4x^3 + 6x^4 + 1) by (x + 3)?

Back

The coefficients are 6, -4, 0, 3, 1.

Tags

CCSS.HSA.APR.D.6

Front

What mistake did Cam make when dividing (x^4 + 3x^2 - 4x - 2) by (x - 2)?

Back

Cam did not use a zero placeholder for the x^3 term.

Tags

CCSS.HSA.APR.D.6

Front

What is the result of dividing (4x^4 + 4x^3 - 9x^2 - x + 2) by (x - 1)?

Back

The result is 4x^3 + 8x^2 - x - 2.

Tags

CCSS.HSA.APR.D.6

Front

When dividing a polynomial by (x - 1), what number should be used in synthetic division?

Back

The number to use is 1.

Tags

CCSS.HSA.APR.D.6

Front

What is the remainder in synthetic division?

Back

The remainder is the last value obtained after performing synthetic division, representing what is left over after the division.

Tags

CCSS.HSA.APR.D.6

Front

How do you factor a polynomial after synthetic division?

Back

After synthetic division, the quotient can be factored further if it is a polynomial of degree 2 or higher, often using methods like factoring by grouping or applying the quadratic formula.

Tags

CCSS.HSA.APR.D.6