Synthetic Polynomials

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

• 0

• 1

• 2

• 3

( 2x - 8)²

• 4x² + 64

• 4x² -16x + 64

• 4x² + 16x - 64

• 4x² - 64

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

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

• 2x² - x - 2

• 2x³ - x² - 2x

• 2x² + 15x + 54 + 208/x+4

• 2x³ + 15x² + 54x + 208

Use synthetic division to determine whether the first polynomial is a factor of the second.

• Yes

• is

• No

• is not

Use synthetic division to determine whether the first polynomial is a factor of the second.

• No

• is

• is not

• Yes

-2x²+4x+48 ÷ x+4

• -2x+12

• 2x+12

• -4x+9

• 4x+9

(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

Use synthetic division

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54

• Yes, (x-2) is a factor.

  There is a remainder.

• No, (x-2) is not a factor.

  The remainder is zero.

• Yes, (x-2) is a factor.

  The remainder is zero.

• No, (x-2) is not a factor.

  There is a remainder. 

Answer explanation

Two ways to solve:

Synthetic division using x = 2

OR

Remainder Theorem: (recommended) Evaluate for x=2 to find the remainder!