17 - 20

Question 1

define

what is synthetic division?

Answer 1

it involves dividing one polynomial by another in the same way you divide numbers

Question 2

define

what is the quotient, the remainder, and the divisor in the number, 18 ½?

Answer 2

18 is the quotient
1 is the remainder
2 is the devisor

Question 3

example

the expression (6x - 5)/(x+2) is equivalent to

Answer 3

1. use synthetic division
   6 - 17/(x+2)
2. plug in numbers, such as x = 2
   (6(2) - 5)/(2+2) = 7/4

Question 4

define

what is the remainder theorem

Answer 4

whenever a polynomial is divided by a monomial, which has a form of ax + b, the remainder can be found by plugging in to the polynomial the value of x that makes the monomial equal to 0

Question 5

example

5x^2 - 4x + 1
divided by
x + 2
what is the remainder?

Answer 5

1. using remainder theoremx
   x - 2 = 0
   x = 2
2. plug x = 2 into polynomial
   5(2)^2 - 4(2) + 1 = 13

Question 6

example

what is the remainder in the expression, 5x + 6 + B/(x-2)?

Answer 6

B is the remainder

Question 7

technique

what is the remainder of (x^2 -3x + 2)/(x-2)?

Answer 7

1. using remainder theorem
   x - 2 = 0 -> x = 2
   2^2 - 3(2) + 2 = 0
2. since remainder is 0, x - 2 is a factor of x^2 - 3x + 2.

Question 8

example

is x + 1 a factor of x^3 + 1?

Answer 8

1. using remainder theorem
   x + 1 = 0 -> x = -1
2. plug in x = -1
   (-1)^3 + 1 = -1 + 1 = 0
   remainder is 0
   therefore, x + 1 is a factor of x^3 + 1

Question 9

define

what is a complex number?

Answer 9

when imaginary number, i or √-1, is used in an expression

Question 10

technique

when faced with a fraction containing i in the denominator,

Answer 10

multiply both the top and bottom of the fraction by the conjugate of the denominator

Question 11

define

what is a conjugate

Answer 11

to get the conjugate, reverse the sign in between an expression
e.g. 5 - 4i
conjugate = 5 + 4i

Question 12

define

what is the absolute value of x

Answer 12

the distance x is from 0

Question 13

confusing concept

can the absolute value be negative

Answer 13

no, since the absolute value of anything is the distance of it from 0, it is always positive

Question 14

example

how many integer values of x satisfy |x| < 4?

Answer 14

1. Consider all possible numbers, both positive and negative.
2. Every integer between -3 and 3 work, a total of 7 integer values

Question 15

technique

in absolute value word problems, start with

Answer 15

1. the midpoint of the desired interval and subtract it from the variable.
2. think of this as the “distance or “error” away from the midpoint of the interval

Question 16

confusing concept

graph y = |x|

Answer 16

V shape

Question 17

technique

one way to narrorw down answer choices for graphs:

Answer 17

obtain points that are easy to calculate
e.g. y = |2x - 1|
1. y intercept = |2(0) - 1| = 1
(0,1) must be on the graph and POE
2. x intercept = 1/2
(0.5, 0) and POE

Question 18

define

what is the exterior angle theorem

Answer 18

an exterior angle is formed when any side of a triangle is extended; an exterior angle is always equal to the sum of the two angles in the triangel furthest from it

Question 19

confusing concepts

when two lines are parallel,

Answer 19

vertical angels are equal
alternate interior angles are equal
corresponding angles are equal
same side interior angles are supplementary, meaning their sum equal to 180 degrees

Question 20

define

total angle of triangle

Answer 20

180 degrees

Question 21

define

total angle of quadrilateral

Answer 21

360 degrees

Question 22

define

total angle of pentagon

Answer 22

540 degrees

Question 23

define

total angle of hexagon

Answer 23

720 degrees

Question 24

key formula

for any polygon, the sum of the interior angles is

Answer 24

180(n - 2) where n is the number of sides