Synthetic Polynomials

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

• 0
• 1
• 2
• 3

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

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

• x⁴
• x³
• x²
• x

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

• 0
• -3
• 9
• 5

What should be the order of the polynomial coefficients of the dividend.

(3x - 4x³+ 6x⁴ + 1) / (x + 3)

• 3 0 -4 6 1

• 6 -4 3 1 0

• 6 -4 0 3 1

• -6 4 0 -3 -1

The answer to a division problem is known as the...?

• product
• sum
• difference
• quotient

What is the proper way to write the answer for the following problem? If the dividend was a quartic.

• 2x³-x²-25x+12

• 2x⁴-x³-25x²-12x+0

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x-0

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.

When dividing the polynomials should long or synthetic division be used.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

• Long Division

• Synthetic Division