Polynomial Equations and Factoring

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Presentation transcript:

Polynomial Equations and Factoring Chapter 7 Polynomial Equations and Factoring 7.1 Adding and Subtracting Polynomials Students will be able to find the degree of monomials. Students will be able to classify polynomials. Students will be able to add and subtract polynomials. Monomial – is a number, a variable, or the product of a number and one or more variables with whole number exponents. Degree of a Monomial – is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. The constant 0 does not have a degree.

Find the degree of each monomial. Degree of a Monomial – is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. The constant 0 does not have a degree. Monomial Degree 10 3x 1 5 Not a monomial Reason 5+x A sum is not a monomial A monomial cannot have a variable in the denominator. A monomial cannot have a variable exponent. The variable must have a whole number exponent. Find the degree of each monomial. 2 4=1+3 6=3+3

Polynomial – is a monomial or a sum of monomials Polynomial – is a monomial or a sum of monomials. Each monomial is called a term of the polynomial. A polynomial with two terms is a Binomial. A polynomial with three terms is Trinomial. Binomial Trinomial Degree of a Polynomial – is the greatest degree of its terms. Standard Form – is when the exponents of the terms of a polynomial decrease from left to right. Leading Coefficient – is the coefficient of the first term when you write a polynomial in standard form.

Degree of a Polynomial – is the greatest degree of its terms. Standard Form – is when the exponents of the terms of a polynomial decrease from left to right. Leading Coefficient – is the coefficient of the first term when you write a polynomial in standard form. Degree of a Polynomial – is the greatest degree of its terms. Leading coefficient Degree Constant Term

Write the polynomial in Standard Form, identify the degree, leading coefficient and classify/name the polynomial. Degree = 3 Degree = 1 Leading Coefficient = -1 Leading Coefficient = -9 Name = Trinomial Name = Binomial

Write the polynomial in Standard Form, identify the degree, leading coefficient and classify/name the polynomial. Degree = 4 Degree = 2 Degree = 5 Leading Coefficient = 5 Leading Coefficient = 1 LC= -3 Name = Trinomial Name = Binomial Name = Monomial

Adding and Subtracting Polynomials – Combine like terms Like terms – have the same variable and the same exponent To Combine – just add or subtract the coefficients Vertical Format

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Last One YEH!! But First Let us review what we learned today Students will be able to find the degree of monomials. Students will be able to classify polynomials. Students will be able to add and subtract polynomials. And NOW… Good Job!