200 300 100 300 100 200 300 100 200 300 100 200 300 100 Theorems I LOVE Parametric Equations Factors, Remainders, And Roots (oh my!) Max-MinInequalitiesGraph.

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Presentation transcript:

Theorems I LOVE Parametric Equations Factors, Remainders, And Roots (oh my!) Max-MinInequalitiesGraph It Misc

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?

A nonzero interger factor of the constant coefficient

Parameterize this equation:

Find an equivalent equation without the parameter t:

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

Factor x 3 + 6x 2 - 4x - 24

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

What is the remainder when P(x)=x is divided by x?

1

Is x = -0.5 a root of the polynomial P(x) = x x x x - 10 ?

YES

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?

20,000m 2

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.

~7.41ft 3

Solve | 2x + 3 | < 6

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

Solve x ≥ 3x

x ≤ 1 or x ≥ 2 (1, 2)’ (-∞,1]U[2, ∞)

Solve

x 1 [-2, 1]’ (-∞,-2)U(1, ∞)

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

ODD

What type of polynomial is this a graph of?

Quintic

How many real roots does this quintic have?

Three

Find the expanded quadratic polynomial with real roots with 1+i as one root.

x 2 +2x+2

Given y-intercept = 3 and x-intercept = 2, write a linear equation for the line in intercept form.

TRUE or FALSE: is a polynomial.

FALSE