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Multiplicity, Degrees, Zeros OH MY!
Division
Grab Bag
100

Write a polynomial in standard form with degree 3.

a polynomial written with exponents from greatest to least - highest exponent is a 3

100

P(x)=6x^2+12-5x^5+4x


This polynomial in standard form.


What is 

P(x)=-5x^5+6x^2+4x+12

?

100
The multiplicity for the root x=6 in this polynomial.

f(x)=x^2(x+7)^2(x-6)^5(x+8)^9

What is 5?
100

If the polynomial below is a factor of the other polynomial what is the remainder?

x^2+x-2

(x^3-2x^2-5x+6)/(x-3)


ZERO

100
The classification, by degree and number of terms, of this polynomial.

7x^5-3

What is quintic binomial?
200

The largest exponent seen in a polynomial in standard form.

What is the degree?

200

The end behavior of this polynomial.

f(x)=-6x^4+3x^2+8



What is Down Down?
200
The degree of this polynomial.

f(x)=-6(x+3)^5(x-7)^2(x+4)^8

What is 15?
200
The value of P(2) for this polynomial.

P(x)=x^3-x^2+3x-2

What is 8?
200

What is the root if we know x+6 is a factor?

What is x=-6?

300
The exponent on a factor of a polynomial written in intercept form.
What is the multiplicity of a root?
300

The end behavior of this polynomial.


P(x)=1/2x^7+4x^5+3x-6


What is Down Up?

300

The roots of this polynomial, including their multiplicities.

P(x)=2x^5(x-1)^2(x+4)^3

0 multi. 5

1 mult. 2

-4 mult. 3

300

The quotient of these two polynomials, using synthetic division.


(3x^4+x^3-2x+3)/(x+1)


What is 

3x^3-2x^2+2x-4 ,r.7

?

300

What is the extrema for the following polynomial?


(x^2+5x-3)


What is (-2.5, -9.25)?

400

How many turning points does a degree n polynomial have?

What n-1.

400
The following difference written in standard form.

(6x^7-4x^4+6x)-(3x^7-9x^4+6x^2-3)

What is 

3x^7+5x^4-6x^2+6x+3

 ?
400

Write the zeros, multiplicity and what happens at each zero on the graph.


P(x)=(x+4)^3(x-6)^2(x+1)


-4 multi. 3 - crosses

6 mult. 2 - bounces

-1 multi. 1 - crosses

400

The quotient of these polynomials, using synthetic division.

(x^3+6x^2+11x+8)/(x+1)

What is 

x^2+5x+6, r.2

?

400

What is the range of the following polynomial?

x^4-4x^3+5x+3

[-9.37, infinity)
500

What process allows us to say the remainder when P(x) is divided by (x-k) is P(k).

Synthetic Substitution

500
The end behavior of this polynomial.

f(x)=5x+3x^4-7x^7+3

What is Up Down?
500

What is the degree of this polynomial?

h(x)=x(x+1)^2(x-5)(x+3)^3

Degree = 7

500
The quotient of these polynomials, using long division.

(x^3-64)/(x^2+4x+16)

What is 

x-4

?
500

Name the decreasing intervals for:

x^4-4x^3+5x+3

 .

(-infinity, -0.6) and (0.74, 2.85)