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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
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