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17.1 Understanding Polynomial Expressions
Students will learn to Identify and classify polynomials Write a polynomial in standard form
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Vocabulary Monomial A number, a variable or the product of numbers and variables with whole number exponents Degree of a Monomial The sum of the exponents of the variables in the monomial State the degree of each monomial 5 𝒙 𝟐 - 𝒂 𝟑 𝒃 𝟕 𝟐 𝟑 𝒘 𝒗 𝟒 𝒖 𝟓 𝟕
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What do you think a polynomial is?
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Polynomial A monomial or a sum of monomials
Which of the following are polynomials? - 𝟑 𝟒 pq 𝟖 𝒕 5 – 6x 4 𝒙 −𝟑 -5 𝒙 𝟐 𝒚+𝟕𝒙+𝟐
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Degree of a polynomial The greatest degree of it terms Standard form of a polynomial Write with terms in descending order by degree Leading coefficient Coefficient of term with the highest degree Constant term Term whose variable has degree zero
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2 𝑥 3 −5𝑥𝑦+4𝑦+9 Example: Find the degree of each term.
2 𝑥 3 −5𝑥𝑦+4𝑦+9 degree 3 degree 2 degree 1 degree 0 Find the degree of each term. Find the degree of the polynomial. degree 3 Find the constant term. 9 Find the leading coefficient. 2
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-4x + 9 - 𝒙 𝟐 −𝟐 𝒙 𝟕 Write in standard form. State the degree.
State the leading coefficient. State the constant.
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Classifying by degree Degree Classification Constant 1 Linear 2
Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Polynomial of degree 5 6 Polynomial of degree 6 etc
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Classifying by terms Number of terms Classification 1 Monomial 2
Binomial 3 Trinomial 4 or more Polynomial
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Summary
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Classify by terms and by degree.
3 𝑥 2 −5𝑥 9 −4 𝑥 3 +6 𝑥 2 +3x+7 5𝑥+3 𝑥 4 −2 𝑥 2
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Turn to page 805 in your books
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Homework Page 812 #1-14, 17-19, 25
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