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 Depdendent Variable

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 Dependent Variable

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# Addition and Subtraction of polynomials

A monomial is a number, a variable, or a product of numbers and variables. The following
examples are monomials. The degree of a monomial is the sum of the exponents of the
variables.

 Degree = 1 Degree = 2 Degree = 3 Degree = 6

The degree of a nonzero constant is zero.
Ex: the degree of 7 is 0

Each of the addends of a variable expression is called a term. For example, the following
variable expression:

4x – 3xy + 4z2

The terms are 4x, -3xy, and 4z2. Note that to determine the terms of an expression, subtraction is
re-written as addition of the opposite.

A polynomial is a variable expression in which the terms are monomials.

 A polynomial of one term is a monomial Example: A polynomial of two terms is a binomial Example: A polynomial of three terms is a trinomial Example: A polynomial of four or more terms is simply called a polynomial Example:

The terms of a polynomial in one variable are usually arranged so that the exponents of the
variable decrease from left to right. This is called descending order.

The degree of a polynomial is the degree of the term of largest degree.

The degree of is 3.
The degree of is 4

Polynomials can be added, using either a horizontal or vertical format, by combining like terms.

Simplify: Use a horizontal format.

 Use the commutative and Associative properties of Addition to re-arrange and group like terms. Then combine like terms.

Simplify: Use a vertical format.

 Arrange the terms of each polynomial in descending order with like terms in the same column Combine the terms in each column

Subtraction of polynomials

The opposite of the polynomial (3x2 – 7x + 8) is –(3x2 – 7x + 8)
To simplify the opposite of a polynomial, change the sign of each term inside of the
parentheses.

Polynomials can be subtracted using either a horizontal or vertical format. To subtract, add the
opposite of the second polynomial to the first.

Simplify: . Use a horizontal format.

 Add the opposite of the second polynomial to the first Combine like terms

Simplify: Use a vertical format.

The opposite of 2y2 + 4y – 21 is –2y2– 4y + 21

 Arrange the terms of each polynomial in descending order with like terms in the same column Note that 4y – 4y = 0, but 0 is not written.