Chapter 6 (Alg 2)

Question 1

properties of Exponents

Answer 1

ProductOP a^m a^n = a^m + n
PoaP (a^m)^n = a^m * n 
Poaproduct (ab)^m = a^m b^m
Neg. Exp a^-m = 1/a^m
Zero Exp a^0 = 1
Quotient op a^m/a^n = a^m - n
Power of a Q (a/b)^m = a^m/b^m

Question 2

Scientific Notation

Answer 2

c * 10^n where c is from 1 to 9

Question 3

Standard form of a polynomial

Answer 3

Terms written in decending order from left to right
Leading Coefficient belongs to the first term
Exponent of the first term is the degree
a term with no coefficient is the constant term

Question 4

End behavior

Answer 4

what happens to f(x) as x gets very large or very small
If Deg. even and Coe. +; f(x) approaches + inf. as x approaches + inf. or - inf.
If Deg. even and Coe. -; f(x) approaches - inf. as x approaches - or + inf.
If Deg. odd and Coe +; f(x) approaches - inf as x approaches - inf. f(x) approaches + inf. as x approaches + inf.

Question 5

Adding and Subtracting Polynomials

Answer 5

add coefficients of like terms, subtract polynomials of like terms

Question 6

Multiplying and Dividing Polynomials

Answer 6

to multiply two polynomials, multiply each term of the first polynomial by each term of the second polynomial

Question 7

Special Product Patterns

Answer 7

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

Question 8

Polynomial long division

Answer 8

Follow same steps as you do to divide whole numbers

Question 9

Special Product patterns

Answer 9

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Question 10

Factor by grouping

Answer 10

pairs of terms that have a common monomial factor
{}
ar + rb + sa + sb = r(a + b) + s(a + b) = (r + s)(a + b)

Question 11

Quadratic form

Answer 11

au^2 + bu + c where u is an expression in terms of x

Question 12

Repeated solution

Answer 12

A polynomial function of degree n has exactly n solutions

Question 13

The Fundamental Theorem of Algebra

Answer 13

If f(x) is a polynomial of degree n where n>0, then the equation f(x) = 0 has at least one root in the set of complex numbers

Question 14

The Fundamental Theorem of Algebra (Corollary)

Answer 14

If f(x) is a polynomial of degree n where n>0, then the equation f(x) = 0 has exactly n solution provided each repeated solution is counted inducidually

Question 15

Local maximum

Answer 15

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

Question 16

Local minimum

Answer 16

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

Question 17

Polynomial Models

Answer 17

in a real-world model, a local maximum on the graph often indicates a value that maximizes the quantity being modeled.