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POLYNOMIALS 7-5 & 7-6

POLYNOMIALS 7-5 & 7-6. Today I will learn… I can classify polynomials by their degree and number of terms . I can combine like terms using addition . I can combine like terms using subtraction. . What is a Monomial???.

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POLYNOMIALS 7-5 & 7-6

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  1. POLYNOMIALS7-5 & 7-6 Today I will learn… I can classify polynomials by their degree and number of terms. I can combine like terms using addition. I can combine like terms using subtraction.

  2. What is a Monomial??? A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents.

  3. What is a Polynomial??? A polynomial is a monomial or a sum or difference of monomials. 7x5+ 4x2 – 6x + 9 11x7 + 3x3 x3 + x2 – x + 2 6 7a3b2 – 2a4 + 4b –15 2m 3x – 2

  4. What do we CLASSIFY in life? • Sports  Division IA, IIA, IIIA… • Drivers Licenses

  5. Classifying Polynomials • The degree of a polynomial is the highest exponent in a polynomial. Degree: 3 x3 + 3x + 2 Degree: 2 2x2 – x + 2 Degree: 1 4x + 1 1 6 x0 Degree: 0

  6. 0 Constant 1 Linear Quadratic 2 Cubic 3 Quartic 4 Quintic 5 6 or more 6th,7th,degree and so on Classifying Polynomials by Degree

  7. Term #: 1 2 3 4 Term #: 2 1 3 Classifying Polynomials by the Number of Terms 2. The number of terms in a polynomial is the sum of the number of monomials in the expression. 6x – 7x5 + 4x2 + 9 4 terms y2 + y6 – 3y 3 terms

  8. Terms Name 1 Monomial 2 Binomial 3 Trinomial Polynomial 4 or more Classifying Polynomials by the Number of Terms

  9. Example: Classifying Polynomials Classify each polynomial according to its degree and number of terms. A. 5n3 + 4n Cubic Binomial Degree 3 Terms 2 B. – 5y2 + 2y – 9 Quadratic Trinomial Degree 2 Terms 3 C. –2x Degree 1 Terms 1 Linear Monomial

  10. Standard Form of a Polynomial The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. ***Write polynomial in order of degree biggest  smallest

  11. y2 + y6 – 3y y6 + y2 – 3y Degree 6 6 1 2 1 2 The standard form is y6 + y2 – 3y. The leading coefficient is 1. Example: Writing Polynomials in Standard Form Write the polynomial in standard form. y2 + y6 − 3y Find the degree of each term. Then arrange them in descending order:

  12. 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 2 Degree 1 5 2 5 1 0 0 –7x5 + 4x2 + 6x + 9. The standard form is The leading coefficient is –7. Example: Writing Polynomials in Standard Form Write the polynomial in standard form. 6x – 7x5 + 4x2 + 9 Find the degree of each term. Then arrange them in descending order:

  13. How do the following expressions compare? (3y) + (4y) and (3y)(4y) -4x5x and -4x + 5x y2 + 3y2 and y2 3y2 (4m3)(-6y4) and (4m3) + (-6y4)

  14. Adding and Subtracting Polynomials… A.K.A. Combining Like Terms Group “Like Terms” Together **use table if it helps 2s2 + 3s2 + s 2s2 + 3s2 s2 =5s2 5s2 + s s 1s =s

  15. Don’t Forget… - (4a2 – 6a2 + 1)

  16. Together On Your Own

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