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TheoremsI LOVE

ParametricEquations

Factors, Remainders,

And Roots(oh my!)

Max-Min Inequalities Graph It

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Misc.

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How many real roots must an odd degree

polynomial have to have in order to have real

coefficients?

1

If a polynomial with real coefficients has a factor (x-(1-2i)), what must one of the other factors be?

(x-(1+2i))

The rational root theorem tells us that if a polynomial

has a root of the equation

then p must be what? p

xq

A nonzero interger factor of the constant

coefficient

Parameterize this equation:

3 5 6y x x

3

( )

( ) 5 6

x t t

y t t t

Find an equivalent equation without the

parameter t:

2

( ) 1

( ) 4

x t t

y t t t

2

2

( 1) 4( 1)

6 5

y x x

y x x

Find the domain and range for x-y equation, given the

following parametric equation

42

4)(

2)(

t

tty

ttx

}82|{:

}84|{:

yyR

xxD

Factor x3 + 6x2 - 4x - 24

(x-2)(x+2)(x+6)

What is the remainder What is the remainder when P(x)=xwhen P(x)=x200200+1 is +1 is

divided by x?divided by x?

11

Is x = -0.5 a root of the Is x = -0.5 a root of the polynomialpolynomial

P(x) = xP(x) = x4 4 + 9.5x+ 9.5x3 3 - 7.5x- 7.5x2 2 - 26x - 10- 26x - 10??

YESYES

Two numbers add to 5. What is the largest

possible value of their product?

6.25

Suppose an area of farmland along a straight stone wall is

to be fenced. There are 400m of fencing available.

What is the greatest rectangular area that can be

enclosed?

20,000m2

An open box is to be made from a 3 foot by 8 foot piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the

box can have.

~7.41ft3

Solve | 2x + 3 | < 6

-4.5 < x < 1.5(-4.5,1.5)

Solve x2 + 2 ≥ 3x

x ≤ 1 or x ≥ 2(1, 2)’

(-∞,1]U[2, ∞)

Solve

0)2(

)1(

x

x

x < -2 or x > 1[-2, 1]’

(-∞,-2)U(1, ∞)

Is the function in the graph even, odd, or neither?

ODDODD

What type of polynomial is this a graph of?

QuinticQuintic

How many real roots does this quintic have?

ThreeThree

Find the expanded quadratic polynomial

with real roots with 1+i as one root.

x2+2x+2

Given y-intercept = 3 and x-intercept = 2, write a linear

equation for the line in intercept form.

132

yx

TRUE or FALSE:

is a polynomial.( )P x x

FALSE