Ch. 9 & 10 Flashcards Preview

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Flashcards in Ch. 9 & 10 Deck (41)
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1

polynomial

an expression that can be written as a monomial/sum of monomials w/ whole # exponents

2

degree

(of a polynomial) the largest exponent

3

what can a polynomial NOT be?

it can't have negative or fractional exponents it can't have variables in denominators

4

polynomial equation

an equation that can be written w/ a polynomial as 1 side & 0 as the other side

5

standard form

(of polynomials) from left to right, exponents go from largest to smallest

6

rational number

can be written as quotient of 2 integers

7

rational expression

an expression that can be written as the quotient of 2 polynomials

8

rational equation

an equation with only rational expressions on both sides

9

Product of Powers Rule

am • an = am + n

10

Quotient of Powers Rule

am/an = am - n

a does not equal 0

11

how to factor polynomials

  1. facor out any GCF's
  2. factor normally (ax2 + bx + c)

12

ratio of the volume of two spheres

is equal to the ratio of the cubes of their diameters

13

Power of a Power Rule

(am)n = amn

14

Power of  Product Rule

(ab)n = anbn

15

Power of a Quotient Rule

(a/b)n = an/bn

b does not equal 0

16

how to solve rational equations

  1. find LCD of all 3 & make the denominators all the same and cancel them out OR find LCD of left side denominators, make them the same, and then cross multiply
  2. simplify

17

extraneous solution

when a solution is not a solution of the original equation

(test it)

18

point of no return

the point where it would take as much time to return to the starting point as to continue on to the destination. 

use t = d/r

d/r = d/r

19

cubic function

a polynomial function of degree 3

20

zero of a function

value of x that makes y = 0, same as x-intercept

21

double zero

cubic function w/ a squared factor

22

triple zero

a cubic function w/ a cubed factor

23

y = (x - 2)3

intersects x-axis once

24

y = (x - 2)2(x + 1)

intersects x-axis twice

25

y = (x - 2)(x + 1)(x + 4)

intersects x-axis three times

26

steps to solve a cubic equation w/out graphing

  1. put y on left side and set it to 0
  2. find the GCF of the right side if possible and factor it out
  3. if ax2 + bx + c format, use quadratic formula

27

how to solve cubic equations w/ calculator

1. input equation

2. find x-intercept (where y = 0)

28

square root of negative number

becomes i • pos. square root

29

parametric equation

equations where two variables are expressed in terms of a 3rd variable

30

parameter

3rd variable of a parametric equation