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U2 – 2.1 POLYNOMIALS Naming Polynomials Add and Subtract Polynomials Multiply Polynomials

U2 – 2.1 P OLYNOMIALS Naming Polynomials Add and Subtract Polynomials Multiply Polynomials

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Text of U2 – 2.1 P OLYNOMIALS Naming Polynomials Add and Subtract Polynomials Multiply Polynomials

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  • U2 2.1 P OLYNOMIALS Naming Polynomials Add and Subtract Polynomials Multiply Polynomials
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  • D EFINITIONS Exponents Power Simplify Terms Monomials Polynomials
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  • M ORE D EFINITIONS Like Terms Constant Degree Coefficient Binomial Trinomial
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  • EXAMPLE 1 Identify polynomial functions Name each polynomial by degree (highest exponent), the number of terms (and expression that can be written as a sum, the parts added together) leading coefficient (number in front of the variable with highest degree) SOLUTION a. The degree is 4, number of terms is 2, leading coefficient 2
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  • EXAMPLE 1 Identify polynomial functions Name each polynomial by degree, the number of terms, and leading coefficient. a. 10a SOLUTION a. The degree is 1, the number of terms is 1, and the leading coefficient is 10.
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  • EXAMPLE 1 Identify polynomial functions Name each polynomial by degree, the number of terms, leading coefficient SOLUTION a. The degree is 5, the number of terms is 3, and the leading coefficient is 3.
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  • EXAMPLE 1 Identify polynomial functions Name each polynomial by degree, the number of terms, and leading coeffcient. a. 3 SOLUTION a. The degree is :None and the number of terms is 1, leading coefficient none.
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  • GUIDED PRACTICE for Examples 1 and 2 State the polynomials degree, terms, and leading coefficient. 1. f ( x ) = 13 2 x SOLUTION f ( x ) = 2 x + 13 It is a polynomial function. Standard form: 2x + 13 Degree: 1 Leading coefficient of 2. Number of terms : 2
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  • GUIDED PRACTICE for Examples 1 and 2 2. p ( x ) = 9 x 4 5 x 2 + 4 SOLUTION It is a polynomial function. Standard form:. p ( x ) = 9 x 4 5 x 2 + 4 Degree: 4 Leading coefficient of 9. Number of terms : 4
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  • GUIDED PRACTICE for Examples 1 and 2 3. h ( x ) = 6 x 2 + 3 x SOLUTION h ( x ) = 6 x 2 3 x + The function is a polynomial function that is already written in standard form will be 6 x 2 3 x + . It has degree 2 and a leading coefficient of 6.
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  • EXAMPLE 1 Add polynomials vertically and horizontally a.Add 2 x 3 5 x 2 + 3 x 9 and x 3 + 6 x 2 + 11 in a vertical format. SOLUTION a. 2 x 3 5 x 2 + 3 x 9 + x 3 + 6 x 2 + 11 3 x 3 + x 2 + 3 x + 2
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  • EXAMPLE 1 Add polynomials vertically and horizontally (3 y 3 2 y 2 7 y ) + ( 4 y 2 + 2 y 5) = 3 y 3 2 y 2 4 y 2 7 y + 2 y 5 = 3 y 3 6 y 2 5 y 5 b. Add 3 y 3 2 y 2 7 y and 4 y 2 + 2 y 5 in a horizontal format.
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  • EXAMPLE 2 Subtract polynomials vertically and horizontally a. Subtract 3 x 3 + 2 x 2 x + 7 from 8 x 3 x 2 5 x + 1 in a vertical format. SOLUTION a. Align like terms, then add the opposite of the subtracted polynomial. 8 x 3 x 2 5 x + 1 (3 x 3 + 2 x 2 x + 7) 8 x 3 x 2 5 x + 1 + 3 x 3 2 x 2 + x 7 5 x 3 3 x 2 4 x 6
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  • EXAMPLE 2 Write the opposite of the subtracted polynomial, then add like terms. (4 z 2 + 9 z 12) (5 z 2 z + 3) = 4 z 2 + 9 z 12 5 z 2 + z 3 = 4 z 2 5 z 2 + 9 z + z 12 3 = z 2 + 10 z 15 Subtract polynomials vertically and horizontally b.Subtract 5 z 2 z + 3 from 4 z 2 + 9 z 12 in a horizontal format.
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  • GUIDED PRACTICE for Examples 1 and 2 Find the sum or difference. 1. ( t 2 6 t + 2) + (5 t 2 t 8) SOLUTION 6 t 2 7 t 6 t 2 6 t + 2 + 5 t 2 t 8
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  • GUIDED PRACTICE for Examples 1 and 2 2. (8 d 3 + 9 d 3 ) ( d 3 13 d 2 4 ) SOLUTION = (8 d 3 + 9 d 3 ) ( d 3 13 d 2 4) = (8 d 3 + 9 d 3 ) d 3 + 13 d 2 + 4) = 9 d 3 3 d 3 + 13 d 2 + 8 d 3 + 4 = 8 d 3 + 13 d 2 + 8 d + 1
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  • TRY THE FOLLOWING PROBLEMS
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  • ANSWERS TO ADDITION PROBLEMS
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  • TRY THE FOLLOWING PROBLEMS
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  • ANSWERS TO THE SUBTRACT PROBLEMS
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  • Multiply Polynomials 1.3(2)2.3(2x) 3.3x(2x)4.3x(2x+1) 5.3x+1(2x)6.(3x+1)(2x+1) 7.(3x+1)(2x+1)(x+1)
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