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Teacher 2019.notebook 1 October 29, 2019 Nov 1411:21 AM Polynomials
Teacher 2019.notebook
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October 29, 2019
Nov 1411:21 AM
Polynomials
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Nov 1411:26 AM
Polynomials are mathematical expressions that are made up of both letters and numbers.
3x + 2y + 6z
COEFFICIENTS(the number in front
of the variable)
VARIABLES(the letters in the
polynomnial)
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Nov 1412:03 PM
Binomials are polynomials with exactly two terms.
Trinomials are polynomials with exactly three terms.
Monomials are polynomials that only have one term. Remember that a term is a number or letter (variable) that is separated by a plus, minus or equal sign.
There are different types of polynomials:
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Technically a polynomial is a sum of one or more monomials.
# of Terms Name: Example:
1 monomial 4x
2 binomial 4x + 7
3 trinomial 4x + 7 - 3y
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Nov 169:49 PM
How can you remember the various names of polynomials?
3xy2 5x - 1 3x + 5y2 - 3
Monomial Bionomial Trinomial
(1 term) (2 terms) (3 terms)
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Polynomial or "Not a Nomial"3x
2xy-2
5-6x3 + (1/2)y
1/x3x/8
2
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Polynomials are written in STANDARD FORM, which means they are written in descending order. This means the largest exponent goes first.
3x5 - 2x3 + 7x - 1
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Polynomial Number of Terms
Name of Polynomial
2x3x + 4 -2y-7x + 8y4a - b2
1
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Write the following polynomials in standard form:x4 - 2x2 + 3x + 5x5
3x2 - 8x + 3x6 + 5x3
11x12 - 23x5 + 33x11 - 15x7
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Degree of Polynomials
The degree of a polynomial with only one variable is the largest exponent of that variable.
Example: 4x3 - x + 3 The degree is 3 (the largest exponent of x)
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The degree of a monomial is the sum of the exponents of the all of the variables in that monomial.
2x3y2z5
Why is the above a monomial? ___________
What is the degree of this monomial? _____
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What is the degree of this monomial?
• The exponents of each variable are 4 and 2. 4 + 2 = 6• The degree of the monomial is 6.• The monomial can be referred to as a 6th degree monomial.
**Remember the degree of a monomial is the sum of the** exponents of the variables in the monomial.
Or
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A degree of a polynomial is found by determining the degree of each term. The largest value found, is the degree of the entire polynomial.
2x2y3z4 + 4xy - 3
Determine the degree for each term!term 2 term 3
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A constant has no variable. It is a 0 degree polynomial. 2
4x + 1 This is a 1st degree polynomial.
5x2+2x-14 This is a 2nd degree polynomial.
Notice that all of the above polynomials only have one variable in each...an x
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Nov 1412:30 PM
Polynomials and Algebra Tiles
Use the following:
x2 -x2 x -x 1 -1
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Dec 512:47 PM
Write the following polynomials with algebra tiles. Remember that a solid figure represents a positive value.
1. 3x2 - 2x + 7
2. -2x2 + x -3
3. 5x -2
