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Simplify Expressions

100

#1

(-4m²n)⁴ * 1/6 m^-10n^-4

128/3m²

200

#3

(6x-7x²+7)-(5x²+2x-2x³-1)

2x³-12x²+4x+8

300

#4

(y+4)³-2y(y-1)

y³+10y²+50y+64

400

#5

(3k-6)(k²-k+7)

3k³-9k²+27k-42

500

#6

-8c⁶d⁴+56c⁴d²-24c²d

--------------------------

8c²d

-c⁴d³+7c²d-3

Factor Polynomials

100

What factoring method would you use?

a²-b²

Difference of squares

200

What factoring method was used to get this?

(a+b)(a²-ab+b²)

Sum of cubes

a³ + b³

300

#7 Factor completely

9x³+21x²

3x²(3x+7)

400

#8 Factor completely

3n⁴-147

3(n²+7)(n²-7)

500

#12 Factor completely

216pq-p⁷q

pq(6-p²)(36+6p²+p⁴)

Polynomial Graphs

100

#17 What is the parent function?

f(x)= x³+8x²+16x+7

Cubic

f(x)=x³

200

#17 What are the end behaviors?

f(x)= x³+8x²+16x+7

as x -> -infinity, f(x) -> - infinity

as x -> +infinity, f(x) -> +infinity

300

#17 What are the domain and range?

f(x)= x³+8x²+16x+7

Both are all real numbers.

400

#21 Identify the zeros

f(x)=3x³(x-1)²(x-8)

x={0,1,8}

500

#23 The graph of a polynomial function has zeros of 0, 1, and 5/2. Write a function in factored form.

f(x)=x(x-1)(2x-5)

Dividing Polynomials

100

#32 

(x³+x²-71x+9)/(x+9)

x²-8x+1

200

#34

(12a³+2a²-6a-30)/(3a-4)

4a²+6a+6-6/(3a-4)

300

#36

Find f(-2) when

f(x)=3x³-28x²+70

-66

Functions

100

#38 

Given: f(x)=x²+4x-12, g(x)=5x²-2, and h(x)=x+7

Find (f-g)(x)

-4x²+4x-10

200

#39

Given: f(x)=x²+4x-12, g(x)=5x²-2, and h(x)=x+7

Find (h*g)(x)

5x³+35x²-2x-14

300

#40

Given: f(x)=x²+4x-12, g(x)=5x²-2, and h(x)=x+7

Find (h/f)(x) indicate any domain restrictions.

x+7

-----------

(x+6)(x-2)

{xI x is not= -6, 2}

400

#41 

Given: f(x)=x²+4x-12, g(x)=5x²-2, and h(x)=x+7

Find (g o h)(x)

5x²+70x+243

500

#42  

Given: f(x)=x²+4x-12, g(x)=5x²-2, and h(x)=x+7

Evaluate (g+h)(-4)

81