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.

Find the quotient when (2x^3 - 5x^2 + 3x - 1) is divided by (x + 4) using synthetic division.

• 2x^2 - 5x + 15

• 2x^2 - 3x + 15

• 2x^2 - 3x + 5

• 2x^2 - 3x + 10

Answer explanation

To find the quotient using synthetic division, the coefficients of the dividend are used. Performing the division, we get 2x^2 - 3x + 15 as the quotient.

Use synthetic division to divide (6x^4 + 3x^3 - 2x^2 + 5x - 1) by (x - 1).

• Quotient: 4x^3 + 6x^2 + 5x + 9, Remainder: 7

• Quotient: 7x^3 + 8x^2 + 6x + 11, Remainder: 10

• Quotient: 5x^3 + 7x^2 + 3x + 10, Remainder: 8

• Quotient: 6x^3 + 9x^2 + 7x + 12, Remainder: 11

Answer explanation

Using synthetic division, we find the quotient: 6x^3 + 9x^2 + 7x + 12 and remainder: 11, which matches the correct answer choice.

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.

Perform synthetic division to divide (7x^4 + 2x^3 - 5x^2 + 3x + 1) by (x + 1).

• 7x^3 - 5x^2 + 1

• 7x^3 - 5x^2 + 3

• 7x^3 - 5x^2 - 3

• 7x^3 - 5x^2 + 3

Answer explanation

Performing synthetic division, we get the quotient 7x^3 - 5x^2 + 3. Therefore, the correct answer is 7x^3 - 5x^2 + 3.

Find the quotient of (9x^3 - 6x^2 + 4x - 2) divided by (x - 2) using synthetic division.

• 9x^2 + 12x + 28

• 9x^2 + 14x + 28

• 9x^2 + 10x + 28

• 9x^2 + 12x + 18

Answer explanation

Using synthetic division, we find that the quotient is 9x^2 + 12x + 28. Therefore, the correct answer is 9x^2 + 12x + 28.