2/22-23 HA2 Polynomial Synthetic Division

HA2 Notes Synthetic Division of Polynomials

Take notes by hand and annotate.

Vocabulary

• Synthetic Division: A shorthand method of dividing polynomials by a linear binomial using only the coefficients. To use synthetic division the dividend must be in standard form and contain placeholders (terms with a coefficient of zero) for any missing terms. The divisor must be in root form.

Synthetic Division Directions

Synthetic Division Examples

Multiple Choice

 $\left(12x^2+2x-2\right)\div\left(3x-1\right)$  

• 4x-2
  

• 4x-2 R1

• 4x+2

• 4x+2 R1

Multiple Choice

 $\left(x^2-6x-16\right)\div\left(x+2\right)$  

• x-8 R2
  

• x-8
  

• x-6 R10

• x-6

Multiple Choice

 $\left(-5x^2+2x^3-4x-25\right)\div\left(x-4\right)$  

•  $2x^2+3x+8\ R7$  

•  $2x^2-3x+8\ R7$  

•  $2x^3+3x^2+8x\ R7$  

•  $2x^2+3x-8\ R7$