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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!