Polynomial Vocabulary
This feature is based on a polynomial's highest exponent
Degree
What is the "root value" of (x - 4)?
4
(x3 + 2x2 + 5x + 4) + (2x3 + x2 + 4x + 2)
3x3 + 3x2 + 9x + 6
(x + 2)(x - 2)
x2 - 4
(x2 + 4x - 32) / (x -4)
Find Quotient & Remainder.
Q: x + 8
R: 0
The process for multiplying two Binomials. Its a result of the distributive property.
FOIL
How many turning points (max) does a 4th degree polynomial have?
3
(4x3 - x2 +3x - 7) - (4x3 - x2 - 2x + 3)
5x - 10
(3x - 6)(3x + 6)
9x2 - 36
Find f(3).
52
A polynomial with two terms
Binomial
How many zero's (max) does a quadratic polynomial have?
2
(x4 - 4x3 + 2x2 - 3x - 8) + (5x3 - 3x2 + x + 8)
x4 + x3 - x2 - 2x
(x + 3)(x - 5)
x2 - 2x - 15
f(x) = 12x3 - 34x2 - 11x + 29
Find f(3).
14
Cubic
Roots can be found at x = -4 and x = 3. Write the factored form of this polynomial.
(x + 4)(x - 3)
(6x5 - 4x4 + 2x3 - 12x2) - (6x4 + 3x3 - 8x + 4)
6x5 - 10x4 - x3 - 12x2 + 8x - 4
Roots are found at x = -5, 0, and 2. Write the polynomials in Standard Form.
x3 + 3x2 - 10x
f(x) = 12x4 + 40x3 - 33x - 9
Find f(-3).
-18
This describes the direction a function is headed as it extends toward both positive and negative infinity.
End Behavior
A 4th degree polynomial also has a negative leading coefficient. Describe it's end behavior on both ends.
L Falls/Decreasing, R Falls/Decreasing
(1.65x3 - 2.02x2 + 0.43x - 89.90) - (1.01x3 + 3.99x2 - 0.54x - 90.09)
0.64x3 - 6.01x2 + 0.97x + 0.19
Roots are found at x = -4, 2, and 4. Write the polynomials in Standard Form.
x3 + 2x2 - 16x -32
f(x) = 6x4 - 29x3 - 11x2 + 29x - 39
Find f(5).
-44