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Adding and Subtracting PolynomialsAlgebra NotesheetName: _______________________Date: ________________________A _________________ is a number, a variable, or the product of a number and one ore more variables with whole number exponents.The ________________ of a monomial is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is ____. The constant 0 does not have a degree.MONOMIALDEGREE103x12ab21.8m5NOT A MONOMIALREASON5+x2n4ax-1EXAMPLE 1: Finding the Degrees of MonomialsFind the degree of each monomial.a. 5x2b. -12xy3c. 8x3y3d. -3A ___________________ is a monomial or sum of monomials. Each monomial is called a _________ of the polynomial. A polynomial with two terms is a __________________. A polynomial with three terms is a __________________.The _____________ of a polynomial is the greatest degree of its terms. A polynomial in one variable is in ___________________________ when the exponents of the terms decrease from left to right. When you write a polynomial in standard form, the coefficient of the first term is the _____________ _______________________.EXAMPLE 2: Writing a Polynomial in Standard FormWrite 15x-x3+3 in standard form. Identify the degree and leading coefficient of the polynomial.EXAMPLE 3: Classifying PolynomialsWrite each polynomial in standard form. Identify the degree and classify each polynomial by the number of terms.POLYNOMIALSTANDARD FORMDEGREETYPE OF POLYNOMIAL-3z44+5x28q+q5To add polynomials, add like terms. You can use a vertical or horizontal format.EXAMPLE 4: Adding PolynomialsFind the sum.a) 2x3-5x2+x+(2x2+x3-1)b) 3x2+x-6+(x2+4x+10)EXAMPLE 5: Subtracting PolynomialsFind the difference.a) 4n2+5-(-2n2+2n-4) b) 4x2-3x+5-(3x2-x-8)EXAMPLE 6: Solving a Real-Life ProblemA penny is thrown straight down from a height of 200 feet. At the same time, a paintbrush is dropped from a height of 100 feet. The polynomials represent the heights (in feet) of the objects after t seconds. ................
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