Download addition & subtraction of polynomials

ALGEBRA 1
Adding and Subtracting
Polynomials
Mr. J. Grossman
1
VARIABLE EXPRESSIONS


A variable expression contains one or
more variables.
There is not an equal (=) sign.
5 x  4 xy  y  4
2
2
TERMS



5 x  4 xy  y  4
2
The terms are the variables, numbers or
combinations of variables and numbers that
make up the expression.
 There are 4 terms in the given expression.
Variable terms contain variables.
 There are 3 variable terms in the given
expression. What are they?
Constant terms contain only numbers.
 There is 1 constant term in the given
expression. What is it?
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NUMERICAL
2
5 x  4 xy  y  4
COEFFICIENT



Each term contains two parts:
1.
The variable part and
2.
The numerical coefficient
The numerical coefficient is often called simply the
coefficient.

It is the number that multiplies (sits in front of)
the variable(s).
There is always a number in front of a variable.

If you don’t see a number, then the number is 1.
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LIKE TERMS
5x  2 y  6  2 x  2 y  9
3


3
2
Terms that are identical in the variable part (to
include exponent value) are like terms.
 Note: Like signs are different from like terms.
Constant terms are like terms because they have
no variable part and are therefore alike in the
variable part.
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COMBINING LIKE TERMS

Combine or
simplify like
terms by adding
or subtracting
their numerical
coefficients.


Rearrange the
terms if necessary.
Use the sign rules
correctly.
3a  2b  5a
 3a  5a   2b
2a  2b
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Classifying Polynomials

Monomial: an expression that is a
number, a variable, or the product of a
number and one or more variables.




a number: 8,
a variable: x, or
a product of numbers and variables: 8xy
Binomial:

a polynomial with two terms: 2x + 3
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Classifying Polynomials

Trinomial


2 x  5x  7
3
2
a polynomial with three terms
Polynomial

a variable expression in which
the terms are monomials:
5x + 9y – 10 + 6xy
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Classifying Polynomials
Standard Form of a Polynomial
 Written in descending order


Arranging the terms of a polynomial,
according to the exponents, in order from
largest to smallest.
Degree of a Polynomial

The degree of the term with the largest
degree
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Classifying Polynomials




Constant – a polynomial of 0 degree
Linear – a polynomial of 1 degree
Quadratic – a polynomial of 2 degree
Cubic – a polynomial of 3 degree
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Classifying Polynomials
Polynomial
Degree
Name Using
Degree
Nr of
Terms
Name Using Nr
of Terms
7x  4
1
Linear
2
Binomial
3x  2 x  1
2
Quadratic
3
Trinomial
3
Cubic
1
Monomial
0
Constant
1
Monomial
2
4x
5
3
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ADDITION & SUBTRACTION
OF POLYNOMIALS

Add or subtract polynomials by combining
like terms.
 Add or subtract their coefficients
vertical format:
2
3

3
x

7
x

8

3
x

   5x  14 
 3x 2  7 x  8
3x3
 5 x  14
3x3  3x 2  2 x  6
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ADDITION & SUBTRACTION
OF POLYNOMIALS

Add or subtract polynomials by combining
like terms.
 Add or subtract their coefficients
horizontal format:
 2x
3
 6 x  3   7 x  3 x  9 
2
2 x3  7 x 2  6 x  3x  3  9
2 x  7 x  3x  6
3
2
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ADDITION & SUBTRACTION
OF POLYNOMIALS


The minus sign touching the parenthesis of
the second polynomial means that a negative
one is multiplied by the second polynomial.
Perform multiplication before addition.
3
3
2

6
x

4
x

5

2
x

7
x
 6x  2

 
 6 x3  4 x  5  2 x3  7 x 2  6 x  2
 6 x3  2 x3  7 x 2  4 x  6 x  5  2
 8 x3  7 x 2  10 x  7
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ADDITION & SUBTRACTION
OF POLYNOMIALS

Remove each polynomial from
parenthesis, then add
13z
3
 6 z  7   5z  2 z  9
13z
2
 6z  7
3
 5z  2 z  9
2
13z  5 z  8 z  2
3
2
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ADDITION & SUBTRACTION
OF POLYNOMIALS

Polynomials in more than one variable are
added and subtracted by combining like
terms.
3
2 2
3
2 2
5
x
y

2
x
y

4
xy


2
x
y

5
x
y  xy 

 
5 x y  2 x y  4 xy  2 x y  5 x y  xy
3
2
2
3
2
2
7 x y  3x y  5 xy
3
2
2
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ADDITION & SUBTRACTION
OF POLYNOMIALS
Any
questions???
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ADDITION & SUBTRACTION
OF POLYNOMIALS
Let’s Practice
Text pg 459
Problems 1, 9, 15, 21,
28, 35, 39, 40.
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