Dividing Polynomials with Synthetic Division

Perform synthetic division to divide (3x^3 + 5x^2 - 2x + 7) by (x - 2).

• 3x^2 + 11x + 22 + 51/(x - 3)

• 3x^2 + 11x + 22 + 51/(x + 1)

• 3x^2 + 11x + 22 + 51/(x - 2)

• 3x^2 + 11x + 22 + 51/(x + 2)

Answer explanation

The synthetic division process correctly yields 3x^2 + 11x + 22 with a remainder of 51/(x - 2), leading to the correct answer choice.

Divide (4x^4 - 2x^3 + 6x^2 - 8x + 5) by (x + 3) using synthetic division.

• 4x^3 - 14x^2 + 48x - 152 + 461/(x - 3)

• 4x^3 - 14x^2 + 48x - 152 + 461/(x + 3)

• 4x^3 - 14x^2 + 48x - 152 + 461/(x - 5)

• 4x^3 - 14x^2 + 48x - 152 + 461/(x + 2)

Answer explanation

Choose the correct answer that matches the result of dividing (4x^4 - 2x^3 + 6x^2 - 8x + 5) by (x + 3) using synthetic division.

What is the result of dividing (5x^3 - 2x^2 + 4x - 7) by (x + 2) using synthetic division?

• 5x^2 - 12x + 28 - 47/(x + 2)

• 5x^2 - 12x + 28 - 47/(x - 1)

• 5x^2 - 12x + 28 - 47/(x - 2)

• 5x^2 - 12x + 28 - 47/(x + 3)

Answer explanation

The correct answer is 5x^2 - 12x + 28 - 47/(x + 2) obtained by dividing (5x^3 - 2x^2 + 4x - 7) by (x + 2) using synthetic division.

Divide (8x^5 - 4x^4 + 2x^3 - 6x^2 + 9x - 3) by (x - 3) using synthetic division.

• 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 5)

• 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 2)

• 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 4)

• 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 3)

Answer explanation

The correct answer is 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 3) as obtained by dividing using synthetic division.

Use synthetic division to divide the polynomial (2x^3 + 4x^2 - 3x + 1) by the binomial (x - 1).

• 2x^2 + 6x - 3

• 2x^2 + 4x + 3

• 2x^2 + 2x + 3

• 2x^2 + 6x + 3

Use synthetic division to divide the polynomial (2x^4 - 5x^3 + 3x^2 + 4x - 1) by the binomial (x + 1).

• 2x^3 - 7x^2 + 10x - 1

• 2x^3 - 7x^2 + 10x + 6

• 2x^3 - 7x^2 + 10x + 1

• 2x^3 - 7x^2 + 10x - 6

Divide using synthetic division

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/(x - 2)

• 2x² - 9x - 15 - 23/(x - 2)

Divide using synthetic division

(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4 - 12/(x + 3)

• 2x² - 2x + 6 - 23/(x + 3)

• 2x² - 2x + 8 - 20/(x + 3)

• 2x² - 4x + 1

Use synthetic division to divide the polynomial (5x^3 + 2x^2 - 4x + 1) by the binomial (x + 3).

• 5x^2 - 13x + 35 - 104/(x - 3)

• 5x^2 - 13x + 35 + 104/(x + 3)

• 5x^2 - 13x + 35 - 104/(x + 2)

• 5x^2 - 13x + 35 - 104/(x + 3)

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4  R(-12)

• 2x² - 2x + 6  R(-23)

• 2x² - 2x + 8  R(-20)

• 2x² - 4x + 1  R0