Transcript Add & Subtract Polynomials

Adding & Subtracting
Polynomials
Lesson 10.1
Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):
The student will be able to use properties of rational and
irrational numbers to write, simplify, and interpret expressions
based on contextual situations.
4
3
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
·
Make
connection with
other concepts in
math
·
Make
connection with
other content
areas.
The student will be
able to use properties
of rational and
irrational numbers
to write, simplify, and
interpret expressions
on contextual
situations.
- justify the sums and
products of rational
and irrational numbers
-interpret expressions
within the context of a
problem
2
1
0
The student will
With help
Even with
be able to use
from the
help, the
properties of
teacher, the student has
rational and
student has no success
irrational
partial
with real
numbers to write success with
number
and
real number expressions.
simplify expres expressions.
sions based on
contextual
situations.
-identify parts of
an expression as
related to the
context and to
each part
Polynomial:
Poly: Many
Form:
nomial: terms
axk
Where k is a non-negative integer.
This is a polynomial in one variable.
k is the degree of ax.
ax alone has a degree of 1
The constant “a” has a degree of 0.
Degree: the degree of a polynomial is the
largest degree of its terms.
Standard form: terms are written in
descending order from the largest to the
smallest degree.
Coefficient: the integer in front of the
variable. How many you have of each
variable. If no number, you have one.
Put this in standard form.
-4x2 + 3x3 + 2
3x3 – 4x2 + 2
Name the coefficients and degree.
2x3
+
(-1)x2
+5
Coefficients: 2, -1
Degree: 3
-5x2
+ 10x - 3
Coefficients: -5, 10
Degree: 2
Classifying Polynomials
Polynomial
Polynomial
Degree
6
0
Classify
Polynomial
Terms
Mononomial
-2x
3x+1
1
1
Mononomial
Binomial
-x2+2x-5
2
Trinomial
4x3-8x
3
Binomial
2x4-7x3-5x+1
4
Polynomial
Adding Polynomials: add like terms!
You add the coefficients, not the variables!
Horizontal format:
(2x2+x-5) + (x2+x+6)
= 2x2+x2+x+x-5+6
=3x2+2x+1
remove ( )
Vertical format:
line up like terms and add.
(2x2+x-5) + (x2+x+6)
2x2+x-5
+ x2+x+6
3x2+2x+1
remove ( ) and line up like terms.
Subtracting polynomials: use either vertical or
horizontal format.
***Remember to change the signs of every term in the
second polynomial when you remove the ( )!
Vertical format:
(8x4-3x2-11x-3) – (-13x4-3x2+2x-17)
8x4 - 3x2- 11x - 3
13x4+3x2-2x+17
(combine after changing signs)
21x4 -13x+14
Horizontal format:
(8x4-3x2-11x-3) – (-13x4-3x2+2x-17)
Remove ( ) changing the signs in the second
polynomial. You are adding the opposites!
8x4-3x2-11x-3 + 13x4+3x2-2x+17
(now
combine like terms)
21x4-13x+14
Classify this by degree and terms.
4, trinomial
Find the area of the shaded region.
4
x
2
x
2x
A= bh-bh
x
= x  2x – 4 
2
= 2x2 – 2x
=