Polynomial Long Division
Theorems of Algebra
Polynomial Transformations
Solving and Graphing Polynomials
vocabulary
100
Divide 28x3 + 42x2 − 35x by 7x
4x2 + 6x − 5
100
Find the remainder when f(x) = 5x3 + 7x + 5 is divided by x + 2
-49
100
Even or Odd
f(x) = −x3 − 3x
The Function is Odd
100
Determine the zeros of f(x) = (x − 2)(x − 5)(x + 1)
x = −1, 2, 5
100
Symmetrical
A figure is said to be symmetrical when two halves are equal in size and shape.
200
Divide 2x2 + 17x + 35 by x + 5
2x + 7
200
Find the remainder when f(x) = x3 − 14x2 + 51x − 22 is divided by x − 7
-8
200
Determine whether the function f(x) = 3x4 is even or odd.
The function is even because f(−x) = f(x).
200
What are the zeros of f(x) = (x − 5)(x − 4)(x − 2)?
5, 4, 2
200
Monomial
A monomial is a polynomial with exactly one term. This term could be a constant, a variable, or a variable with a coefficient.Example: 9 or y4 or 10x
300
Divide 63x7−108x6−18x5+27x4 by 9
7x4-12x3-2x2+3x
300
Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)?
x=-3
300
f(x) = x3 − 6
f(x) = f(x) + c
This is a vertical shift of 6 units down.
300
One factor of f(x) = x3 − 14x2 + 61x − 84 is (x − 7). What are the zeros of the function?
7, 4, 3
300
Polynomial
A polynomial is an expression consisting of a term or terms that contain at least one variable raised to a positive integer. When a polynomial is set equal to a constant or other polynomial expression, it is a polynomial equation.
400
5x2-60x+35 by 5
x2-12x+7
400
how many zeros does this function have?
f(x) = 2x5 − 3x4 − 5x3 + 9x2 − 10x + 7
5
400
How does the graph of g(x) = −(x − 2)4 compare to the parent function of f(x) = x4?
g(x) is shifted 2 units to the right and reflected over the x-axis.
400
Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1.
5
400
Function
A function is a set of ordered pairs where every
x-coordinate has one, and only one, distinct corresponding y-coordinate. Graphically, a set of ordered pairs is a function if a line connecting those points passes the vertical line test. If a vertical line can be dragged from left to right across the graph without the vertical line crossing more than one point at a time on the graph, the equation is a function
500
Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find 
2x3 − 6x2 − x
500
Determine the zeros of this function.
f(x) = x2 − 14x + 33
x = 11 and x = 3
500
How does the graph of g(x) = (x − 3)3 + 4 compare to the parent function f(x) = x3?
g(x) is shifted 3 units to the right and 4 units up
500
What is the average rate of change from x = 0 to x = 2 for f(x) = 3x3 − 9x2 + 6?
f(0) = 6
f(2) = −6
500
Factor Theorem
The Factor Theorem states that a first-degree binomial is a factor of a function if the remainder is zero when the function is divided by the binomial.