Polynomial Vocabulary
This feature is based on a polynomial's highest exponent
Degree
What is the "root value" of (x - 4)?
4
List the possible rational roots for the following polynomial. x3 - 3x2 + 4x - 6
1, 2, 3, 6, -1, -2, -3, -6
(x2 + 4x - 32) / (x -4)
Find Quotient & Remainder.
Q: x + 8
R: 0
The theorem that allows us to put all the factors of the last term over all the factors of the first term.
Rational Roots Theorem
How many turning points (max) does a 4th degree polynomial have?
3
10 possible rational roots
f(x) = 2x2 - 10x + 37
Is x-3 a factor of f(x)?
no
A polynomial with two terms
Binomial
How many zero's (max) does a quadratic polynomial have?
2
Roots are found at x = -5, 0, and 2. Write the polynomials in Standard Form.
x3 + 3x2 - 10x
f(x) = 3x3 - x2 - 3x + 1
is 1/3 a root?
yes
Cubic
Roots can be found at x = -4 and x = 3. Write the factored form of this polynomial.
(x + 4)(x - 3)
Find the roots of x3 - 2x2 - 11x + 12
x=1, -3, 4
f(x) = 9x4 + 90x3 + 80x2 - 10x - 9
State if (x+9) is a factor
yes
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
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
is 5 a root?
no