Dividing Polynomials Using Synthetic Division

The Lesson Activities will help you meet these educational goals:

  • Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, and use mathematics to model real-world situations.
  • STEM—You will apply mathematical knowledge to analyze real-world situations.
  • 21stCentury Skills—You will use critical-thinking and problem-solving skills.

Directions

Save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.

______

Self-Checked Activities

Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.

  1. Dividing Polynomials Using Synthetic Division
  1. A rectangular cuboid (a solid shape similar to a cube, except the sides are not all the same size) is to be shaped such that its volume is The depth and the height areand respectively. Answer the following questions to use synthetic division to find the length of the cuboid.
  1. The volume divided by the height will give the area of the face of the cuboid (the one resting on the ground). What is the area of this face?

Sample answer:

The volume of the cuboid is and the height of the cuboid is

Therefore, the area of the face is

Using synthetic division, the coefficients of the polynomial are 7, 0, -4, 3, and

k = -1.

-1 / 7 / 0 / -4 / 3
-7 / 7 / -3
7 / -7 / 3 / 0

Therefore, the area of the face is with a remainder of 0.

  1. The area of the face is the product of the length and the depth. Using this information, find the length of the cuboid.

Sample answer:

The area of the face of the cuboid as determined above is

Area = length × depth

Length = area ÷ depth

Therefore, the length is

Using synthetic division, the coefficients of the polynomial are 7, -7, 3, and k = -4.

-4 / 7 / -7 / 3
-28 / 140
7 / -35 / 143

Therefore, the length of the rectangular cuboid is given by

  1. An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.

Sample answer:

The current passing through the element has a fixed value, 2 amps, and a variable part, x.

Heat generated =

Resistance = or

-2 / 10 / 0 / 0 / 80
-20 / 40 / -80
10 / -20 / 40 / 0

Resistance =

-2 / 10 / -20 / 40
-20 / 80
10 / -40 / 120

Therefore, the resistance will be

1