•1.) Monomial - a number, variable, or product of either with only exponents of 0 or positive integers.
•y, -x, ab, 1/3x, x2, 8, xy2, (abc2)3
Examples
Special Note• 1.) Monomial - No monomial
has a variable as an exponent, nor does it have a variable in the denominator of a fraction.
• 3/y, xa
Terms to write down• 2.) Polynomial - is the sum or
difference of monomials.
• Any Monomial is also a polynomial
• a-b, 7-x, -2x2 +xy-3, • 1/8x - xy2, r + 9, 6
Examples
Adding Polynomials•Add 5x + 7 and 8 - 2x
Adding Polynomials•Add 5x + 7 and 8 - 2x
Subtracting Polynomials•subtract 3a + b from 7a + 5b
Subtracting Polynomials•Subtract 3a + b from 7a + 5b
Adding Polynomials•Add c2 + 5c + 4 and 3c - 7
c2 + 5c + 4 3c - 7
c2 + 8c - 3
c2 + 5c + 3c + 4 - 7
Adding Polynomials•Add c2 + 5c + 4 and 3c - 7
c2 + 5c + 43c - 7
c2 + 8c - 3
Monomials•Have one term such as:
•6, 7a, 5x2, -4m3n2
-4m3n2
Binomials•Have two terms such as
•5x + 3, 6y2 - 2,
•a - b, 2x2y - 3xy2 The terms are separated by one operation sign (+ or -)
Trinomials•Have three terms such as:
• 3x2 + 5x - 6• -3m + m3 -2
The terms are separated by two operation signs (+ or -)
Be ready to answer the following questions:
•1.) What separates the terms of a polynomial?
•2.) How many signs separate the terms of a trinomial?
Which of these are monomials?
•1.) x2 y2, x2 /y2, 1/7, ax2 + bx + c, 1/x + y
Which of these are Polynomials?
•1.) x2 + y2, x3, x2 - 1/3, ax2 + bx + c, 1/x + y
Clssifying Polynomial
•Polynomials are Classified by degree.
•The Degree is determined by the exponents of the terms.
The degree of a Monomial•Is the sum of the exponents of the variables of the monomial.
x3 3x3 y2 5
Monomial Degree
3x3 y2 532x3 y2 5
The degree of a Monomial•Is the sum of the exponents of the variables of the monomial.
Monomial Degree
x 1x y 2
9 0
The degree of a Polynomial•Is the highest degree of any of its terms after the poly has been simplified. Polynomial Degree
3x2 + 5x + 7 2
The degree of a Polynomial Polynomial Degree
3x2 + 5x + 7 23x2 -9xyz +y+z 3x + y + 7 12x2 +7x -3y-2x2 1
Descending order of Polynomials• From the highest degree to the
lowest degree of the terms.
•3x2 + 5x + 7
•3x3 + 5x2 - 2x + 7
Ascending order of Polynomials• From the lowest degree to the
highest degree of the terms.
•7 + 5x + 3x2
•7 - 2x + 5x2 + 3x3
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