Unit 4 Vocabulary Flashcards
Remainder Theorem
If a polynomial of f(x) is divided by x-k, then the remainder is r=f(k)
Factor Theorem
A polynomial f(x) has a factor of x-k if and only if f(k)=0.
Rational Zero Theorem
(a.k.a- rational root test) If f(x) is a polynomial function with integer coefficients then every rational zero of f(x) has the form:
p/q = factor of the constant term/factor of the coefficient
When should I use Rational Zero Theorem
- ) When the degree is higher than 2
2. ) When a problem cannot be factored using “normal” methods.
Does the Rational Zero Theorem always work? why..
No because the roots are sometimes imaginary or irrational.
The Fundamental Theorem of Algebra
If f(x) is a polynomial of degree “n” where n is greater than 0, then the equation f(x) = 0 has at least one root in the set of complex numbers.
Corollary to Fundamental Theorem of Algebra
An nth degree polynomial always has exactly “n” solutions in the set of complex numbers.
if (x-k) has an odd exponent…
the graph crosses the x-axis at x=k
if (x-k) has an even exponent…
the graph is tangent to (only touches) the x-axis at x=k.
Turning points
A point higher or lower then all nearby points on a graph
Local Maximum
the y-coordinate of a turning point if the point is higher then all nearby points
Local Minimum
the y-coordinate of a turning point if the point is lower then all nearby points
The graph of every polynomial function of degree n has
n-1 turning points.
If a polynomial function has n distinct, real zeros, then the graph has
n+1 turning points.
