Unit 4: HDPS and Factoring

End Behavior

100

Determine the end behavior of f(x)=2x⁴-3x+1

Concave up 

200

Determine the end behavior f(x)=-2/3(t^2-5t+3)

falls to the left and falls to the right

300

Write the following end behavior in proper notation f(x)=2x^3-3x+1

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

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

400

Write the following end behavior in proper notation f(x)=-5x - 6x³ -2x⁶ 

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

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

Find polynomial in factored form with given zeros and multiplicities or the graph

100

Find a polynomial with the given zeros and a total degree of 5: 0,2

x³(x-2)²

200

What's the equation of the graph on the board 

-(x+2)²(x-1)

300

Find a polynomial with the given zeros: -2 (passes) , 2 (Bounces), -5 (passes) , 4 (passes) which rises left and falls right

-(x+2)(x-2)²(x+5)(x-4)

400

What is the equation of the graph on the board 

x²(x+1)(x-2)

500

Find a polynomial with the given zeros: 0 (bounces),2 (passes), -5 (bounces)

x²(x-2)(x+5)²

Terminology zeros and multiplicity

100

find the zero(s) and the multiplicity for each zero f(x)=x³+2x²-4x-8

zeros:x=-2 multip: 2; x=2 multip:1

200

What is the GCF of of  -7x⁴+14x²+21

-7

300

How many roots does the polynomial x(x-6)(x+2)³ have and why?

5 - factored form add exponents

400

find the zero(s) and the multiplicity for each zero f(x)=x⁴+25x²

zero:x=0 mutip:2 , x=5i multip: 1, x= -5i, multi: 1

Factoring Completely

100

6x³-9x²+2x-3

(3x²+1)(2x-3)

200

x⁴-100x²

x²(x+10)(x-10)

300

-3x³-3x²+27x+27

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

400

x³-4x²+16x-64

(x²+16)(x-4)

500

x⁴-5x³-25x²+125x

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