Polynomial Parts
Identify each piece of this term: 7x2
7: Coefficient
x: variable
2: Exponent
Can you add 3x8 + 6x8?
Yes
What method did we discuss for multiplying polynomials?
The box method.
Evaluate if x = 2:
f(x) = 3x + 1
7
True or False: 3x7 + 2x2 - x + 1 is an even polynomial.
Is x1/2 a monomial?
No, cannot have fractions in the exponent. (No negative exponents or radicals, either.)
Add:
(3x2 + 4x + 7) + (2x2 + 6x + 4)
5x2 + 10x + 11
Multiply:
(x + 1)(x - 3)
x2 - 2x - 3
Find f(3) if f(x) = x2 + 5x
24
Describe the end behavior of a polynomial with a degree of 7.
up-down or down-up
What is the degree of: 34x6 - 11x12 + 3x - 9
12
Add:
(6x2 - 8x - 3) + (2x2 - 2x + 5)
8x2 - 10x + 2
Multiply:
(x2 + 2x + 3)(x + 1)
x3 + 3x2 + 5x + 3
Find f(2) if f(x) = x3 + 2x - 7
5
Describe the end behavior of a polynomial with a degree of 6.
up-up or down-down
List the polynomial in standard form:
13x8 - 7x + 10x10 + 9
10x10 + 13x8 - 7x + 9
Subtract:
(7x2 + 8x + 6) - (3x2 + 2x + 3)
4x2 + 6x + 3
Multiply:
(x2 + 7x - 3)(x - 2)
x3 + 5x2 - 17x + 6
Find f(5) if f(x) = 2x3 - 4x2 + 10
160
Low curves on a graph are called...
minimums
Name the degree, how many terms, and list in standard form:
12x9 + x2 - 16x4 + 2x - 6
Degree: 9
Terms: 5
Standard Form: 12x9 - 16x4 + x2 + 2x - 6
Subtract:
(10x2 - 2x + 1) - (3x2 - 5x - 12)
7x2 + 3x + 13
Multiply:
(3x3 + 4x - 7)(x3 + 2x - 2)
3x6 + 10x4 - 13x3 + 8x2 - 22x + 14
Find f(0) if f(x) = 12x6 + 4x2 - 10x - 21
-21
High curves on a graph are called...
maximums