Is It or Isn't It?
Degree, LC and End Behavior
Polynomial Division
End Behavior
Random Polynomial Functions
100

The part of f(x) = 2x^3 + x^-3 -2 that makes this NOT a polynomial function.

What is the negative exponent?

100

The end behavior for the function: 

y = -3(3-2x)^2(x+4)

What is as x --> infinity, y --> -infinity 

                x --> - infinity, y --> infinity 

100

When y = 2x^3 + 3x^2-12x - 12 is divided by (x+4) the result is (x-3)(2x+1). 

y = (x-3)(2x+1)(x+4) is written as...

What is a product of linear factors?

100

As x --> infinity, the right hand end behavior of y = x^6 - 36 is?

What is infinity?

100

The intersection of the polynomials 

f(x) = (2x+1)(x-3)

g(x) = x(x-3)

What is (3,0) and (-1,4)?

200

The powers on the x-values all need to be this for the function to be a polynomial function.

What is positive integers zero and above? What are whole numbers?

200

The type of polynomial where the end behavior goes in the same direction?

What is an even degree?

200

Write y = x^3 + 2x^2 -9x - 18 as a product of linear factors if (x + 2) is a factor. 

What is y = (x +2)(x-3)(x + 3)?

200

The two parts of a polynomial function that you look at in order to determine the end behavior.

What are the degree and leading coefficient?

200

Write the following polynomial in standard form:

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

What is -27x^3+36x^2+33x+6?

300

The end behavior of this function follows this pattern for the degree and leading coefficient: f(x) = 5 - 6x^4 - 7x^8 + 12x^2 - 3x

What is even negative? 

300

The degree of the polynomial function: 

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

What is 5th degree?

300

What is the other factor of y =x^3 +8x^2 -17x - 15 if (x+3) is a factor?

What is x^2 + 5x -32?

300

Using the end behavior sketch the graph of 

y = x^4(8-x)^3

What is as x --> Infinity, y --> - infinity

                x --> - Infinity, y --> infinity 

300

The vertical intercept of y = 8(x-3)(2x-1)(x+3)

What is 72?

400

The part of polynomial division that tells you whether or not the the divisor is a factor?

What is the remainder?

400

What term will give you all the information you need for the end behavior ?

What is the leading term?

400

What is the remainder of f(x) = x^3 - 2x^2 - 3x - 6 if the polynomial is divided by (x + 2)?

What is -16?

400

If a polynomial function has an even degree and a positive leading coefficient, both the left and right ends of the function approach this.

What is positive infinity?

400

For the function, f(x) = x^3 + 6x^2 - x + 2 , f(1) = 8. What is the remainder when f(x) is divided by x - 1

What is 8?

500

How will you decide if (3x - 4) is a factor of 3x^4 + 2x^3 - 20x^2 -8x + 32?

What is f(4/3)? If it's 0 it's a factor! 

What is long division? If there is a remainder or not!

500

The leading coefficient for the function f(x) = 6x - 3x^2 - 12x^3 +18

What is -12?

500

Given f(-4) = 3, f(0) = 36, f(-2) = 0, and f(9) = 0, write the equation of the polynomial in standard form if as x --> infinity, f(x) --> - infinity, x --> - infinity, f(x) --> - infinity. 

What is  f(x) = -2x^2+14x +36 ?

500

The degree and leading coefficient for a polynomial when f(x) -> - infinity as x -> - infinity and f(x) -> + infinity as x -> + infinity

What is odd degree and positive leading coefficient?

500

A function curves down and touches the x-axis exactly x = 4 then curves back up again. What is a possible factor of the graph?

What is (x - 4)^2? (or to any even degree)

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