Transcript Chapter 4

§ 4.4
Addition and
Subtraction of
Polynomials
Identifying Polynomials
A polynomial x is an expression containing
the sum of a finite number of terms of the
form axn, for any real number a and any
whole number n.
Examples:
Non-Examples:
a.) x2 + x – 3
a.) x2/3 + x
b.) 4y
b.) 8y-5
c.)
3z5
+
7w2
1
+2
c.)
3z5
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+
7w2
1
+ x
2
Identifying Polynomials
A polynomial is written in descending order (or
descending powers) of the variable when the
exponents on the variable decrease from left to
right.
Example:
5x6 + 4x3 – 7x + 9
A polynomial with one term is called a monomial. A
binomial is a two-termed polynomial. A trinomial is
a three-termed polynomial.
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Identifying Polynomials
The degree of a term of a polynomial in one
variable is the exponent on the variable in that term.
Example:
5x6 (Sixth) 4x3 (Third) 7x (First) 9 (Zero)
The degree of a polynomial is the same as that of
its highest-degree term.
Example:
5x6 + 4x3 – 7x + 9 (Sixth)
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Adding Polynomials
To add polynomials, combine the like terms
of the polynomials.
Example:
a.)
(5x – 6) + (2x – 3) =
5x – 6 + 2x – 3 =
3x – 9
b.)
(x2y + 6x2 – 3xy2) + (-x2y – 12x2 + 4xy2) =
x2y + 6x2 – 3xy2 + (-x2y) – 12x2 + 4xy2 =
– 6x2 +xy2
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Subtracting Polynomials
1. Use the distributive property to remove parentheses.
(This will have the effect of changing the sign of
every term within the parentheses of the
polynomial being subtracted.)
–(4x3 + 5x2 – 8) = – 4x3 – 5x2 + 8
2. Combine like terms.
Example:
(5x – 6) – (2x – 3) = 5x – 6 – 2x + 3 = 3x – 3
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