Factoring Polynomials
Synthetic Division
Long Division
Polynomial Identities
Complex Numbers
100

Factor the polynomial:

x3+7x2+10x 

x(x+5)(x+2)

100

Use Synthetic Division to divide the following equation:

(x2-3x-40)/ (x+5)

x-8

100

Divide the polynomial by long division.

(3x2+7x-20) / (x+4)

3x-5

100

What is the polynomial identity for a sum of cubes? (you can use any two variables-but recall I used a & b in the equation during the lesson)

a3+b3=(a2-ab+b2)

100

Factor the polynomial: (you will get a complex number solution)

8x3=1

1/2, (-1 +/- i sqrt3)/4

200

Factor the polynomial:

9x3+6x2-3x

3x(3x-1)(x+1)

200

Use Synthetic Division to solve the following equation:

(x3+3x2-x+2)/(x-1)

x2+4x+3, R:5

200

Use Long Division to solve the following equation:

2x3-3x2-18x-8) / (x-4)

2x2+5x+2

200

What is the general equation for a difference of squares? (Remember, I used a & b in the equation during the lesson)

a2-b2=(a+b)(a-b)

200

Factor the polynomial: (you will get a complex number solution)

x4-12x2=64

x=+/-4,+/-2i

300

Factor the polynomial and find the zeros:

3x3+12x2-3x=12

x=-4,-1,1

300

Use Synthetic Division to solve the following equation:

(x3+27) / (x+3)

x2-3x+9

300

Use Long Division to solve the following equation:

(x2-7x+10)/ (x+3)

x-10, R:40

300

The following is an example of which identity? 

8x3-1=(2x-1)(4x2+2x+1)

Difference of cubes

300

Factor the polynomial: (you will get a complex number solution)

x4+4x2=12

+/- sqrt2, +/- i sqrt 6

400

Factor the polynomial to find the zeros. You may need to use the quadratic equation.

12x3=60x2+75x

x=0, (5 +/- 5sqrt2) /2

400

Use Synthetic Division to solve the following equation:

(x4+3x3+x+4) / (x+3)

x3-3x2+12x-35, R:109

400

Use Long Division to solve the following equation:

(x3+5x2-3x-1) / (x-1)

x2+6x+3, R:2

400

The following is an example of which identity? 

x2+10x+25=(x+5)2

Perfect Square Trinomials 

400

Factor the polynomial: (you will get a complex number solution)

81x3-192=0

x= 4/3, (-2 +/- 2i sqrt 3)/3

500

Factor the polynomial to find the zeros. 

x3+1=x2+x

x=-1,1

500

Use Synthetic Division to solve the following equation:

(x5+1) / (x+1)

x4-x3+x2-x+1

500

Use Long Division to solve the following equation:

(2x2+x-7) / (x-5)

2x+11, R:48

500

The following is an example of which identity?

x3-125

Difference of cubes

500

Factor the polynomial: (you will get a complex number solution)

x3+x2+x+1=0

x=-1,+/-i