Synthetic and Long Division Polynomials

• x + 5 + (2/2x - 4)
• x - 8
• x - 5 + (3/2x - 4)
• x + 5

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

• True

• False

• Only for the dividend

• Only for the divisor

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0

• 2

• 4

• 6

What is the quotient when (10n² - 37n - 12) is divided by (n - 4)?

• (10n - 3)

• (3n - 10)

• (10n + 3)

• (3n + 10)

• 2x³ + 3x + (7/x-4)
• 2x² + 3x + 8 + (7/x-4)
• 2x² + 3x + 8
• 2x² - x + 10 + (6/x-4)

If 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0

• -3

• 9

• 5

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656

• p(2) = 652

• p(2) = -64

• p(2) = -368

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.

Divide Using Long Division:

(10x⁴+4x³-8x²+3x+10) / (2x²-4x)

• 5x²+12x+20+((83x+10)/(2x²-4x))

• 5x²+12x+20

• 10x⁴+3x+10

• 7x⁴+11x³+102x²+30x+22+(83 / 2x²-4x)

Is this division problem worked correctly?

• This is correct!

• This is incorrect, and error occurs on the 2nd line!

• This is incorrect, and the error occurs on the 4th line!

• This is incorrect, and the error occurs on the 3rd line!