Unit 4 Vocabulary Flashcards Preview

Math Vocab > Unit 4 Vocabulary > Flashcards

Flashcards in Unit 4 Vocabulary Deck (14)
Loading flashcards...
1
Q

Remainder Theorem

A

If a polynomial of f(x) is divided by x-k, then the remainder is r=f(k)

2
Q

Factor Theorem

A

A polynomial f(x) has a factor of x-k if and only if f(k)=0.

3
Q

Rational Zero Theorem

A

(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

4
Q

When should I use Rational Zero Theorem

A
  1. ) When the degree is higher than 2

2. ) When a problem cannot be factored using “normal” methods.

5
Q

Does the Rational Zero Theorem always work? why..

A

No because the roots are sometimes imaginary or irrational.

6
Q

The Fundamental Theorem of Algebra

A

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.

7
Q

Corollary to Fundamental Theorem of Algebra

A

An nth degree polynomial always has exactly “n” solutions in the set of complex numbers.

8
Q

if (x-k) has an odd exponent…

A

the graph crosses the x-axis at x=k

9
Q

if (x-k) has an even exponent…

A

the graph is tangent to (only touches) the x-axis at x=k.

10
Q

Turning points

A

A point higher or lower then all nearby points on a graph

11
Q

Local Maximum

A

the y-coordinate of a turning point if the point is higher then all nearby points

12
Q

Local Minimum

A

the y-coordinate of a turning point if the point is lower then all nearby points

13
Q

The graph of every polynomial function of degree n has

A

n-1 turning points.

14
Q

If a polynomial function has n distinct, real zeros, then the graph has

A

n+1 turning points.