Polynomials, Monomials, Binomials, Trinomials
Three types of polynomials are defined: monomials, binomials, and trinomials.
Examples of Simplifying Expressions Written in Parentheses
Using more than one of the rules for exponents to simplify expressions written with parentheses.
Factor 7x2y2 4xy2 - 8x2y
Practice factoring: 7x2y2 4xy2 - 8x2y
Factor 18x - 12y
Using the distributive law to factor the polynomial 18x - 12y is demonstrated.
Factor 72m3n2p5 - 48mn5p3
Practice factoring: 72m3n2p5 - 48mn5p3
Thoroughly Check for Common Factors
Be thorough when checking for common factors, especially when factoring by inspection. You have not factored completely until no common factors remain.
Rational Numbers Review
In a rational number, the numerator can be any integer and the denominator can be any integer except zero. A rational expression is like a rational number. In a rational expression, the numerator and denominator can be any monomial or polynomial.
Examples of Simplifying Expressions
Expressions that include a negative exponent can be simplified by first rewriting the expression with positive exponents.
Factor: 3xy – 9x 6y - 18
Sometimes a greatest common factor for a polynomial expression can be found before any terms are grouped. This can lead to parentheses inside of parentheses, which can be confusing. Using brackets as a substitute for a set of parentheses can help to...
Multiplying Two Factors with the Same Base
The rules for exponents begin with the rule for multiplying two factors with the same base.