Dividing Polynomials Synthetic Division

• 2x² + 2x - 4  R(-12)

• 2x² - 2x + 6  R(-23)

• 2x² - 2x + 8  R(-20)

• 2x² - 4x + 1  R0

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!

What should be the correct order of the coefficients when setting up synthetic division for (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

• 0

• 2

• 4

• 6

Answer explanation

A placeholder is needed for every missing degree in the polynomial.

(for this example, we need x^5, x^4, x^2, and x)

(x²+4x-45)⁄(x+9) (use synthetic division)

• x+5

• -x+5

• -x-5

• x-5

(2x⁴-7x³+14x²-55x+21)

___________________________

(2x-7)

use synthetic division

• x²+7x-3

• 2x³+14x-6

• x²-7x+6

• 2x³+7x-3

What is the proper way to write the answer for the following problem? 

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x+0

What number goes in the yellow area?

• 9

• -9

• 6

• -6

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