Dividing Polynomials Using Synthetic Division

What does this tell me?

• f(-2)= -27 and -27 is the remainder

• -2 is a solution of the function

• (x+2) is a factor of the function

• (x-2) is a factor of the function

When can we use Synthetic Division to divide polynomials?

• Any time we need to divide.

• When dividing by a binomial

• When dividing by a trinomial

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13

• 2x³ + 4x² +3x - 1

• 2x² - 4x + 3 - 13/x-2

• 2x² + 4x + 3 - 1/x-2

2x³ - 5x² + 3x + 7 ÷ x - 2

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/(x - 2)

• 2x² - 9x - 15 - 23/(x - 2)

Which would be better to use here?

• Long division

• Synthetic division

3x³ + 5x - 1 ÷ x + 1

• 3x³ - 3x² + 8x - 9

• 3x² - 3x + 8 - 9/x+1

• 3x² + 3x + 8 + 7/x+1

• 3x³ + 3x² + 8x + 7

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.

What number goes in the yellow area?

• 9

• -9

• 6

• -6