Download Terms and Factoring - Scarsdale Public Schools

January 30, 2015
Terms and Factoring
A monomial is a number, a variable or a product of a number
and a variable where all exponents are whole numbers.
A monomial has NO variable in its denominator. It has one term. (Prefix mono means one)
13, 3x, -57,
x²,
4y²,
-2xy, or 520x²y²
(notice: no negative exponents, no fractional exponents, constants are monomials)
A binomial is an expression that is the sum of two monomials. It has two unlike terms.
(Prefix bi means two)
3x + 1,
x² - 4x,
2x + y, or y - y²
A trinomial is an expression that is the sum of three monomials. It has three unlike
terms. (Prefix tri means three)
x2 + 2x + 1,
3x² - 4x + 10,
2x + 3y + 2
A polynomial is an expression of the sum of one or more unlike terms.
(poly implies many)
x2 + 2x,
3x3 + x² + 5x + 6,
4x - 6y + 8
Notes on this page taken from:
http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/smono.htm
January 30, 2015
Multiplying a Polynomial by a Monomial
Recall the Distributive Property:
3(4x - 8) - 2(x2 + 1)
After simplifying with the Distributive Property, each
term that was multiplied now has the multiplier as one
of its factors.
Simplify:
4y2 ( 5y4 + 3y2 − 2 )
Use the Distributive Property and the
exponent rule for multiplying powers with
the same base
January 30, 2015
Examples
2
4b (5b + b + 6 )
-7h (3h2 − 8h − 1)
2
2x (x − 6x + 5)
January 30, 2015
"Reverse" the Distributive Property
2x + 6
7y - 7
January 30, 2015
January 30, 2015
Factoring a Polynomial using the GCF
1) To factor a polynomial, identify the Greatest Common Factor between each of the terms.
2) Mentally Divide each term of the polynomial by the GCF
3) Write the result as the product of the GCF and
the remaining terms of the polynomial.
January 30, 2015
January 30, 2015
NOTE: When factoring a polynomial, your
expression (product of a monomial and
polynomial) should multiply back to the
original expression!