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Chapter 2 Definitions

Section 2-1 Section 2-2 Sections 2-3/2-4

Sections 2-5/2-6

Section 2-7

If a polynomial P(x) has a squared factor such as (x-c)2,

then x=c is a…?

Definitions 100

Double Root

Defintions100

Any value of x for which P(x)=0 is a ____ of the equation?

Definitions 200

Root

Definitions 200

Linear and quadratic functions belong to a family of functions

known as…?

Definitions 300

Polynomial Functions

Definitions 300

The maximum or minimum values of the quadratic function

f(x)=ax2+bx+c occurs at…?

Definitions 400

-b/2a

Defintions 400

The following steps are for ________?

1.Start with the leading coefficient 2.Repeat the following until the last

coefficient is reached:a. Multiply by the value of xb. Add the next coefficient

Definitions 500

Synthetic Substitution

A 500

Classify the following polynomial function as linear, quadratic, cubic, quadratic, or quintic. Also, give its leading term, leading coefficient, and degree.

h(x)= 8-5x3

2-1100

Cubic;Leading term: -5x3

Leading coefficient: -5Degree: 3

2-1 100

State weather the function is a polynomial function. Give the zeroes of the function, if they

exist.X2-3x-4

____________

X2+1

2-1 200

It’s not a functionZeros: -1, 4

2-1 200

Find the value of the function (remember 1= ). Simplify the

answer.

h(x)=2x2-5x+6; h(1+i)

2-1 300

1-i

2-1 300

If P(x)= 3x3-7x2+2x+3, use synthetic substitution to find

P(-2/3)

2-1 400

-7/3

2-1 400

Find the value of the function (remember1= ). Simplify

the answer. x3-9x; ( )

2-1 500

2-1 500

Find the remainder when x5-2x3+x2-4

2-2 100

R=-4

2-2 100

Find the quotient and the remainder when the first

polynomial is divided by the second.

x3-2x2+5x+1; x-1

2-2 200

x2-x+4; R=5

2-2 200

Which of the following are factors of P(x)=x3-5x2+3x+9

a) x+2 b)x+3c) x-3

2-2 300

C

2-2 300

DAILY DOUBLE

2-2 400

DAILY DOUBLE

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Find the remaining roots2x4-9x3+2x2+9x-4=0;

Roots: x=-1, x=1

2-2 400

2-2 400

x=4; x=1/2

Find the quotient and the remainder when the first

polynomial is divided by the second.

x5+3x2+4; x2+2x+1

2-2 500

x3-2x2+3x-1;R=-x+5

2-2 500

If a polynomial P(x) is a squared factor such as (x-2)2, then x=c is a double root of P(x)=0. What can you infer about the graph?

2-3/2-4 100

It will be tangent to the x-axis (at x=c)

2-3/2-4 100

Sketch the graph of the equation y=(x+1)(x-2)(x-4)

2-3/2-4 200

2-3/2-4 200

Factor the polynomial function and sketch its graph

F(x)=x4-x2

2-3/2-4 300

2-3/2-4 300

Factor the polynomial function and sketch its graph F(x)= x4-2x3+2x-1

(Hint: x=1 is a triple root).

2-3/2-4 400

F(x)= (x-1)3(x+1)

2-3/2-4 400

A farmer wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other three

sides.

a)Express the area in terms of x and state the domain of the area function.

b) Find the value of x that gives the greatest area.

2-3/2-4 500

2-3/2-4 500

a) A(x)=-2x2+120x or x(120-2x)

D= 0<x<60

b) x=30

Solve x3-x2-5x+2=0 by using a graphing calculator.

2-5/2-6 100

x=-2, x=0.4, x=2.6

2-5/2-6 100

Solve x4-3x2=9 by using a graphing calculator.

2-5/2-6 200

2-5/2-6 200

X=-2.20, x=2.20

2-5/2-6 300

Solve x3+5x2-4x-20=0 by grouping.

2-5/2-6 300

x=2, x=-2, x=-5

Solve 2x4-x2-3=0 using the quadratic form.

2-5/2-6 400

X= ± i, ±

2-5/2-6 400

According to the rational root theorem, what are all the roots of

P(x)= 3x4+13x3+15x2-4=0 ?

2-5/2-6 500

x=-2 (double root), x=

2-5/2-6 500

Tell whether the following statement is true or false:

Some cubic equations have no real roots

2-7 100

False

2-7 100

Find the sum and product of the roots of the given equation:

4x2-3x+6=0

2-7 200

Sum: 3/4

Product: 3/2

2-7 200

Find a quadratic equation with roots 2±3i.

2-7 300

x2-4x+13=0

2-7 300

Find a cubic equation with integral coefficients that has the

given roots:

3 and 7-i

2-7 400

x3-17x2+92x-150=0

2-7 400

Find a cubic equation with integral coefficients that has no quadratic term and as one

of its roots.

2-7 500

x3-25x+66=0

2-7 500

The Final Jeopardy Category is:

Chapter 2

Please record your wager.

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Suppose you have 102 m of fencing to make two side-by-side rectangular

enclosures, as shown. What is the maximum area that you can enclose?

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x

433.5 m2

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