Polynomial Vocab
A value where the graph crosses or touches the x-axis.
What is a zero (root/x-intercept)?
Even degree, positive leading coefficient → both ends go this direction.
What is up?
Dividing polynomials using a simplified method when dividing by x−c
What is synthetic division?
The vertical asymptote of 1/x
What is x=0?
The first step when solving rational equations.
What is find the LCM?
The term in a polynomial with the highest power.
What is the leading term?
Odd degree, negative leading coefficient → left end goes ___, right end goes ___.
What is up, down?
The remainder when dividing by x−3 s equal to this.
What is f(3)?
The horizontal asymptote of 1/x
What is y=0
Why must solutions be checked?
What are extraneous solutions?
A root that causes the graph to “bounce” off the x-axis.
What is an even multiplicity root or doubel root?
A graph crosses the x-axis at x=−2 and touches at x=3. Which has higher multiplicity?
What is x=3
Factor: x2−9
What is (x−3)(x+3)?
The domain of
1/(x-4)
What is all real numbers except x=4
Solve:
1/x=2/(x_+3)
what is x=3
The number of turning points is at most this value for a degree nnn polynomial.
What is n - 1
A polynomial has 3 turning points. What is the least possible degree?
What is 4?
If x=2 is a root, then (x−2) is a ______.
What is a factor?
1/x^2
is this type of function (even or odd).
What is even?
Solve:
2/(x-1)=4/(x+1)
What is x =3
The behavior of a polynomial as x→±∞
What is end behavior?
If both ends of the graph go down, what can you say about degree and leading coefficient?
What is even degree, negative leading coefficient?
Divide (x3−8)÷(x−2)
What is x2+2x+4
As x→0+, the function 1/x goes to _______.
What is positive infinity
Solve:
1/(x+2)+1/(x-2)=0
What is x=0?