Easy
(2x + 5y) + (3x – 2y)
5x+3y
6v(2v + 3)
12v2+18v
3r 2 − 39r + 90
_________________
r 2 − 3r − 70
3r-9
___________
r+7
polynomial
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable
A grandfather, two fathers and two sons went to the movie theater together and everyone bought one movie ticket each. How many tickets did they buy in total?
3 (the grandfather is also a father and the father is also a son)
(x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)
–2x3 + 11x2 + 10x – 10
7(−5v − 8)
-35v-56
x 2 + 2x − 80
____________________
2x 3 − 24x 2 + 64x
x+10
__________
2x2-8x
trinomial
consisting of three terms
A cell phone and phone case cost $110 in total. The cell phone costs $100 more than the phone case. How much was the cell phone?
$105 (not $110)
(x3 + 5x2 – 2x) + (x3 + 3x – 6) + (–2x2 + x – 2)
2x3 + 3x2 + 2x – 8
(2n + 2)(6n + 1)
12n2+14n+2
9x 2 + 81x
______________
x 3 + 8x 2 − 9x
9
_____
x-1
Like terms
Terms with exactly the same variable factors in a variable expression
A duck was given $9, a spider was given $36, a bee was given $27. Based off of this information, how much money would be given to a cat?
$18 ($4.50 per leg)
(7x2 – x – 4) + (x2 – 2x – 3) + (–2x2 + 3x + 5)
6x2 – 2
(4n + 1)(2n + 6)
8n2+26n+6
2v 2 + 10v − 48
______________
8v + 64
v-3
____
4
Binomial
A polynomial of two terms
If you buy a rooster for the purpose of laying eggs and you expect to get three eggs each day for breakfast, how many eggs will you have after three weeks?
Zero, roosters do not lay eggs
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
4x3+x2-3x+1
(5n + 6)(5n − 5)
25n2+5n-30
6v 3 + 42v 2
_______________
2v 2 + 26v + 84
3v2
_______
v+6
Greatest common factor
The greatest factor that divides evenly into each term of an expression
If the zookeeper had 100 pairs of animals in her zoo and if two pairs of babies are born for each and every one of the original animals, and then sadly 23 animal don’t survive, how many animals do you have left in total?
977 animal (100 x 2 = 200; 200 + 800 = 1000; 1000 – 23 = 977)