Polynomials Division

• 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!

• 2x² + 2x - 4  R(-12)

• 2x² - 2x + 6  R(-23)

• 2x² - 2x + 8  R(-20)

• 2x² - 4x + 1  R0

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

• 0

• -3

• 9

• 5

Answer explanation

Two ways to solve:

Synthetic division using x = 2

OR

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

Use synthetic division

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54

• 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)

Divide the polynomial by the monomial.

• 2x⁸-8x²-28x

• 2x⁸-2x²-7x

• 8x⁷-8x-28x

• 2x⁷ -2x -7

Divide \left(x^2+2x-63\right)\div\left(x+9\right)

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54