PolynomialsA polynomial is a monomial or a sum of monomials, eachcalled a term of the polynomial.What is a monomial?A monomial is a number, a variable, or the product of anumber and one or more variables with whole numberexponents. 15x – x3 + 3 Is a polynomialA polynomial can be named by its terms or its degree.
• A one term polynomial is called a monomial.• A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents.• A two term polynomial is called a binomial.• A binomial is the sum or difference of two monomials.• A three term polynomial is called a trinomial.• A trinomial is the sum or difference of three monomials• More than three terms is just called a polynomial.
Degree of a PolynomialThe degree of a polynomial is the greatest degree of itsterms. Leading coefficient 2x3 + x2 – 5x + 12 Degree Constant termWhen a polynomial is written so that the exponents of avariable decrease from left to right.
Terms and DegreesIs it a polynomial?Classify by degree and number of terms.• 15x – x3 + 3•9• 2x2 + x – 5• 6n4 – 8n• n-2 – 3• 7bc3 + 4b4c
Addition and Subtraction• Addition• Combine like terms• (2x3 – 5x2 + x) + ( 2x2 + x3 –1)• (3x2 + x – 6) + (x2 + 4x + 10)• Subtraction• Add the opposite• Combine like terms• (4n2 + 5) – (-2n2 + 2n – 4)• (4x2 – 3x + 5) – (3x2 – x – 8)
MULTIPLY AND DIVIDEPOLYNOMIALSChapter 9 section 2
Multiplying a monomial by a polynomial• Use the distributive property.• 2x3 (x3 + 3x2 – 2x + 5)• x (7x2 + 4)• 3x2 (2x3 – x2 + 4x – 3)
Multiplying a binomial by a binomial• FOIL• First times first• Outer times outer• Inner times inner• Last times last(x – 4) (3x + 2)
Multiplying a binomial by a binomial• (3a + 4) ( a – 2)• (4n – 1) (n + 5)
Multiplying a binomial by a trinomialUse the box method• (2x2 + 5x – 1) (4x – 3) 2x2 5x -1 4x -3• Combine like terms