Transcript Polynomials - hancockhighmath

Polynomials
Algebra I


Remember: Monomials are separated
by______ or ______ signs.



Monomial = One term – A number, a variable,
or a product of numbers and variables.
Binomial = Two terms – 2 monomials
separated by a + or – sign.
Trinomial = Three terms – 3 monomials
separated by + or – signs.
Identity as a monomial, binomial,
trinomial
1)
2)
3)
4)
5)
6)
5x2
4abc
3x + 2
3x2 – 8xy
a2 + 2ab + b2
5x2 – 2x + 7
1)
2)
3)
4)
5)
6)
Monomial
Monomial
Binomial
Binomial
Trinomial
Trinomial


Remember: Monomials are separated
by______ or ______ signs.
To find the degree of a monomial,
add the exponents on the variables (from each monomial),
then see which one has the largest sum.
7) 3x  5
2
2
0
Do not add
across a
“+” or “-”
sign!!!!
8) y  y  3x m
7
7
6
6
4
4
4+4=8
7) Largest
number is 2
(degree is 2)
8) Largest sum is
8
(degree is 8)
9) x  x y z  z
5
5
3 6
2
5+3+6=14
The largest number (sum) is 14, so the degree of
this trinomial is 14
Place in ascending order according to
(x)
10)  5 x  x  4 x  2
2
3


2  x  5x 4x
2
3

Ascending means to go
from least to greatest
Remember to bring
along sign that is in
front of number
Now which terms
variable has the
smallest exponent?
Place in descending order according to
(y)
11) 24 x y  12 x y  6 x
2
3
2
4


12x y  24x y  6x
3
2
2
4

Descending means
to go from greatest
to least
Remember to bring
along sign that is in
front of number
Now which terms
variable has the
largest exponent for
“y”?
REMEMBER – look at the exponents on each terms variable,
If the term doesn’t have a variable, it’s degree is ZERO.
12) Write each polynomial in descending
(going down) order and give the degree.
2 x  3x  3x  2
2
5
 3x 2x 2 3x 2
5
5
2
1
Largest EXPONENT is 5,
therefore the degree is 5.
0
2  3x  2 x
6
4
3x  2x 2
6
6
4
4
Largest EXPONENT is 6,
therefore The degree is 6.
0
13) Evaluate when x = 2 and y = 3.
 X2
- 7xy + y2
 2  7(2)(3)   3
 4 42 9
2
 29
2