Algebra

Question 1

Synthetic Division

Answer 1

is dividing by a binomial which is in the form x-c where C is the synthetic divisor.

Question 2

Power function

Answer 2

is the simplest polynomial function in the form F(x)=a^nX^n

Question 3

Degree of a polynomial

Answer 3

is the value of the greatest exponent

Question 4

leading co-efficient

Answer 4

is the Co. of the first term of a polynomial in standard form

Question 5

Intermediate Value theorem

Answer 5

states given P(x) with real co-efficients if p(a) and p(b) have opposite signs there is at least one real number “c” beteen A and B such that P(c)=O

Question 6

relative maximum

Answer 6

a point where the function changes from increasing to decreasing

Question 7

relative minimum

Answer 7

is a point where the function changes directions from decreasing to increasing.

Question 8

extrema

Answer 8

are the maximum and minimum value of a function

Question 9

turning point

Answer 9

a point where the function changes directions from increasing to decreasing or switched

Question 10

Prime

Answer 10

a polynomial that cannot be factored

Question 11

sum of CUBES a^3 + b^3

Answer 11

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

Question 12

difference of cubes

Answer 12

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

Question 13

quadratic form

Answer 13

is an expression written as au^2+bu+c for any real numbers and a cannot equal zero

Question 14

reduceable quadratic equation

Answer 14

is any equation that can be written in quadratic form by using u-subsitution

Question 15

remainder theroem

Answer 15

states if a polynomial p(x) iis divided by (x-c) using synthetic division the remainder is equal to p (c)

Question 16

synthetic subsitution

Answer 16

is when the remainder theroem is applied to evaluate a function

Question 17

depressed polynomial

Answer 17

is when the quotient of the polynomial is divided by a binomial resulting in a polynomial which is one degree less.

Question 18

factor therom

Answer 18

states for a polynomial if p(c)=0 then x-c is a factor of p(x)

Question 19

fundamental theorem of algebra

Answer 19

states the polynomial of the n-degree of n has exactly n roots is the set of complex numbers incuding repeated roots

Question 20

Descartes rule of signs

Answer 20

a method used to determine real zeros , negative real zeros, and imaginary zeros.

Question 21

complex conjugate theorom

Answer 21

states if a+bi is a zero of a polynomial, then a-bi is also a zero

Question 22

integral co-efficent

Answer 22

is a constant multiplier of a variable that is an integer

Question 23

Rational zero thrm

Answer 23

states if p(x) is a polynomial with integral co-efficent than every rational zero of p(x)=0 is of the form p/q where p is a factor of the constant Term and q is a factor of the leading factor.