Practice: Synthetic Division and applying the Remainder Theorem

Find the remainder for the following:

 $\frac{x^4-3x^3+4x^2-x+3}{x+2}$  

Find the remainder for the following:

 $\frac{-x^4+2x^3-5x^2+x-7}{x-2}$  

Find the remainder for the following:

 $\frac{7x^5-x+1}{x+1}$  

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

• 0
• 1
• 2
• 3

Answer explanation

Answer explanation

Answer explanation

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

Answer explanation

All exponents need to be listed in decreasing order.

x⁶ + 0x⁵ +0x⁴ +4x³ + 0x² + 0x¹ + 2

What should be the order of the polynomial coefficients if
(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

Answer explanation

Exponents need to to be listed in decreasing order. Remember to fill in 0's when an exponent is missing.

3x¹ - 4x³ + 6x⁴ + 1

What is the next step in synthetic division?

• Bring the 6 down

• Multiply the 9 and 6

• Bring the 9 down

• Add the 9 and 6

Answer explanation

Bring down the first number to start the synthetic division process.

What is the next step in synthetic division?

• Multiply the 9 and 6

• Add the 9 and 6

• Bring down the -48

Answer explanation