  # Polynomial Division , Synthetic Division, Rational Expressions

Long Division  Check: Dividend = (Quotient)(Divisor) + Remainder

Dividing by a monomial : Dividing Two Polynomials with more than One Term:

(1) Write terms in each polynomial in descending
order according to degree.

(2) Insert missing terms in both polynomials with a 0
coefficient.

(3) Use Long Division algorithm. The remainder is a
polynomial whose degree is less than the degree of the
divisor.

Example: Perform the division. Synthetic Division

Synthetic division is used when a polynomial is divided
by a first-degree binomial of the form x − k . Coefficients of Dividend

Diagonal pattern: Multiply by k

Example: Use synthetic division to find the quotient
and remainder. Example: Verify that x − 3 is a factor of Rational Expressions A rational expression is a ratio of two polynomials.

The domain of an expression in one variable is the set
of all real numbers for which the expression is defined.

The domain of a rational expression is the set of all real
numbers that do not make the denominator equal to
zero
.

Reducing Rational Expressions:

Example: Find the domain and reduce the expression to
lowest terms . Domain: Domain:

Multiplication and division : Example: Perform the indicated operations and
simplify. Give restrictions on the variables .  In order to add/ subtract rational expressions we use the
Least Common Multiple (LCM) of the denominators.

To Find the LCM of the Denominators:

1. Factor polynomials that are in the denominators.

2. The LCM is the product of all different factors
which are in the denominators (numbers, variables,
expressions) each raised to the largest power that
appears
on that factor.

Example: Add or subtract, as indicated. Give all
restrictions on the variables. Note: Be aware of the case when the denominators
are additive inverses of each other.

Example: Perform the indicated operations. Mixed Quotients

A mixed quotient (complex fraction) is a quotient of
rational expressions.

Simplifying a Complex Fraction:

Method 1: Multiply both numerator and denominator
by the LCM of the denominators of all
simple fractions and simplify .

Method 2: Perform the indicated additions and/or
subtractions in the numerator and
denominator and then divide.

Example: Simplify the complex fraction (mixed
quotient).  Example: Write the fraction as a sum of two or more
expressions. Example: Perform the indicated operations and simplify Prev Next

Start solving your Algebra Problems in next 5 minutes!      2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of July 28th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor: Step 2 : Let Algebra Helper solve it: Step 3 : Ask for an explanation for the steps you don't understand: Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!         