Definitions
What is the degree of a polynomial?
monomial with the highest exponent
Simplify (2x4)6
64x24
Simplify (15x10 - 5x8) / 5x4
3x6 - r4
What is domain and range?
domain: x values
range: y values
Factor 10x2+5x
5x(2x + 1)
What is a prime polynomial?
A polynomial that cannot be factored
Simplify 8x(2y)3
64xy3
Simplify (4a3 - 8a2 + 4a) / (4a)
a2 - 2a + 1
What does the graph of an even polynomial look like?
Ends of graph are both going up or both going down
Factor x2 - 12x + 32
(x - 4)(x - 8)
What is the lead coefficient?
number in front of the variable with the highest exponent
Simplify (3x2+1) + (8x2-8)
11x2 - 7
Simplify (2x2 + 3x - 14) / (x - 2)
2x + 7
How many zeroes does the graph of the following polynomial have? x3 - 4x2 + 2
Factor x3 + 8
(x + 2)(x2 - 2x + 4)
When do relative minimums or maximums occur?
when the graph changes from increasing to decreasing or decreasing to increasing
Simplify (w + 2y)(w2 - 2wy + 4y2)
w3 + 8y3
Simplify (x3 - 64) / (x - 4)
x2 + 4a + 16
State the degree and leading coefficient of 7x3-4x2+x.
Degree: odd, LC: positive
Prove that 4(x - 5)(x - 10) = 4x2 - 60x + 200 is an identity.
4(x - 5)(x - 10) = 4x2 - 60x + 200
What is the Location Principle?
The Location Principle states that if the value of f(x) changes sign from one value of x to the next, then there is a zero in between those two x-values.
Simplify (4d2t5v-4)(-5dt-3v-1)
(-20d3t2)/(v5)
Simplify (x4 - 3x3 + 5x - 6) / (x + 2)
x3 - 5x2 + 10x - 15 Remainder: 24
Write the end behavior for the polynomial f(x) = x3 - 12x2 + 2x - 4.
as f(x) --> -8, x --> -8
as f(x) --> 8, x --> 8
Solve x4 - 29x2 + 100 = 0.
x = -2, 2, -5, 5