Polynomials

Add/Sub/Multiply

100

Simplify: (9x^2+2x+12)+(7x^2+10x-13)

16x^2+12x-1

200

Simplify: (6x^6-4x^5)-(10x^5-15x^4+8)

6x^6-14x^5+15x^4-8

300

Simplify: (x-3)^2

x^2-6x+9

400

Multiply: 5x(x+2)(3x-7)

15x^3-5x^2-70x

500

Multiply: (x-3)(4x^2-2x+3)

4x^3-14x^2+9x-9

Division

100

Divide: (x^3+10x^2+13x+36)/(x+9)

x^2+x+4

200

Divide: (3x^3+12x^2+11x-2)/(x+2)

3x^2+6x-1

300

Divide: (7x^3-4x^2-400x-100)/(x-8)

(x-8)(7x^2+52x+16)+28

400

Divide: (9x^4+27x^3+23x^2+10x)/(x^2+2x)

9x^2+9x+5

500

Divide: (18x^3-3x^2+x-1)/(x^2-4)

(x^2-4)(18x-3)+73x-13

Binomial Expansion

100

Expand (x+2y)^5

x^5+10x^4y+40x^3y^2+80x^2y^3+80xy^4+32y^5

200

Expand (3x-y)^4

81x^4-108x^3y+54x^2y^2-12xy^3+y^4

300

Expand (5x+y)^4

625x^4+500x^3y+150x^2y^2+20xy^3+y^4

400

Expand (x-6y)^5

x^5-30x^4y+360x^3y^2-2160x^2y^3+6480xy^4-7776y^5

500

Expand (5x-4y)^3

125x^3-300x^2y+240xy^2-64y^3

Factoring

100

Factor 3x^2+4x-4

(3x-2)(x+2)

200

Factor 9x^2-25

(3x+5)(3x-5)

300

Factor 2x^3+4x^2-30x

2x(x+5)(x-3)

400

Factor completely: 4x^2-16x+16

4(x-2)^2

500

Factor completely: x^4+x^3+x+1

(x+1)^2(x^2-x+1)

Graphing

100

What are the transformations from f(x) = x^3 to f(x)=5x^3+3?

Up 3, vertical stretch of 5

200

How many distinct factors in f(x)=x^2(x-2)(x+2)?

3

300

What are the end behaviors for f(x)=x^3?

as x approaches infinity, f(x) approaches infinity. as x approaches neg infinity, f(x) approaches neg infinity.

400

How many turning points and the type of maximum or minimum that they are for f(x)=-(x-4)(x-1)(x+1)(x+2)?

3 turning points, 1 local max, 1 local min, 1 global max

500

Show on a number line the x-intercepts and the sign of the function at each interval for f(x)=-x^2(x-4).

x<0 Positive, 04 Negative