EQ – what is a polynomial, and how can I tell if a term is one?
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Transcript of EQ – what is a polynomial, and how can I tell if a term is one?
![Page 1: EQ – what is a polynomial, and how can I tell if a term is one?](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649f4e5503460f94c6ec40/html5/thumbnails/1.jpg)
PolynomialsPolynomialsEQ – what is a polynomial, and how can I tell if a term is one?
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Terms:Monomial – a number or product of numbers
and variables with exponents that are whole numbers
Examples: 2n, x3, 4a5b6, 7Non Examples: p2.4, 2x, ,
x 2
5
g
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Polynomial – one monomial or the sum or difference of monomials
Examples: , , , x+4Non-Examples: , ,
74
3
1yx
22 42 yx
22 ba 3.010xy
432 yx
yx33
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• Polynomials are classified by their number of terms
One term – monomialTwo terms – binomialThree terms – trinomialFour or more-polynomial
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• Polynomials are also classified by degrees.
• The degree of a polynomial is the same as the term with the greatest degree
524 52 xyxx Degree 2 Degree 5 Degree 1 Degree 0
This polynomial has a degree of 5
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Degrees of a Polynomial
• O - constant• 1st – linear• 2nd-Quadratic• 3rd-Cubic• 4th-Quartic
• Leading coefficient is in front of the highest degree term.
• A constant can be a leading coefficient if by itself.• Standard form –
polynomial in descending order of degrees.
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Simplifying Polynomials
• You can simplify a polynomial by adding or subtracting like terms ( they must have the same variable and the same degree)
• Or you can simplify one using the distributive property
• Leading coefficient - coefficient in front of the term with highest degree.
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Combining like terms
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Try these:
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Using the Distributive Property
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Try these:
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Adding Polynomials
• To add two polynomials, you can combine like terms or line up the like terms and add them vertically.
• Horizontal format• Vertical format
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To add them vertically:
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Try these:
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Subtracting Polynomials
• This is like adding the opposite -- find the opposite of the second number and then add like you did before
• Horizontal format• Vertical format
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Finding the opposite
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To Subtract:
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Try these:
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Multiplying polynomials by
monomials
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Or you may need the distributive property
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Try these:
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Multiplying binomials
Think FOIL (first, outside, inside, and last)
This is the order you will multiply them!
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Check out these examples:
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Try these:
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Factoring Polynomials
• Factoring is dividing out factors that are the same in the polynomial
• Factoring binomials are reversing FOIL.
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Factoring • Taking out the GCF of the terms of a
polynomial.
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Leading coefficient not 1
•
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Special factoring
• Patterns in factoring…
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Try these:
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The End