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 Dependent Variable

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# Polynomials

The Degree of axn

• If a does not equal 0,the degree of axn is n.
The degree of a nonzero constant is 0.The
constant 0 has no defined degree.

Definition of a Polynomial in x

• A Polynomial in x an algebraic
expression of the form • Where and are real
numbers. ,and  n is a non- negative
integer. The Polynomial is of degree n, an
is the leading coefficient, and is the
constant term.

Text Example

Perform the indicated operations and simplify : Solution Group like terms .
Combine like terms .

Multiplying Polynomials

The product of two monomials is obtained by using properties of exponents .
For example Multiply coefficients and add exponents .

Further more , we can use the distributive property to multiply a monomial and
a polynomial that is not a monomial . For example, Multiplying Polynomials When
Neither is Monomial

• Multiply each term of one polynomial by
each term of the other polynomial. Then
combine like terms.

Using the FOIL Method to Multiply Binomials Text Example

Multiply: Solution: Combine like terms.

The product of the Sum and
Difference of Two Terms • The product of the sum and the difference
of the same two terms is the square of the
first term minus the square of the second
term.

The Square of a Binomial Sum • The square of a binomial sum is the first term
squared plus 2 times the product of the
terms plus last term squared.

The Square of a Binomial
Difference The square of a binomial difference is the first
term squared minus 2 times the product of
the terms plus last term squared.

Special Products

Let A and B represent real numbers , variables, or algebraic expression.

 Special Products Sum and Difference of Two Terms Example  Square a Binomial  Cubing a Binomial  Text Example

Multiple: Solution

We will perform the multiplication in part (a) using the (FOIL) method. We Will
multiply in part (b) using the formula for the square of a binomial,  Multiply these binomial using the FOIL method. Combine like terms. Example

Multiply: • Solution: Prev Next