Explanation Given Information: The expression, ( 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 ) ÷ ( 3 y 8 ) . Formula used: 1. While dividing a polynomial by a monomial, each term of the polynomial is divided by the monomial. That is, a + b c = a c + b c ( where c ≠ 0 ) 2. Quotient rule : For any real number a , a m a n = a m − n , where m and n are any integers. 3. Negative exponents: If a is any nonzero real number and n is a positive integer, then a − n = 1 a n . 4. Distributive property: a ( b + c ) = a ⋅ b + a ⋅ c Calculation: Consider the expression, ( 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 ) ÷ ( 3 y 8 ) . Divide each term of the polynomial 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 by the monomial 3 y 8 , 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 3 y 8 = 45 y 7 3 y 8 + 9 y 6 3 y 8 − 6 y 5 3 y 8 + 12 y 4 3 y 8 Simplify the terms as follows, 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 3 y 8 = [ ( 45 3 ) ⋅ ( y 7 y 8 ) + ( 9 3 ) ⋅ ( y 6 y 8 ) − ( 6 3 ) ⋅ ( y 5 y 8 ) + ( 12 3 ) ⋅ ( y 4 y 8

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 4.7, Problem 36E

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To calculate: The value of the expression, (45y7+9y6−6y5+12y4)÷(3y8).

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Chapter 4.7, Problem 35E

Chapter 4.7, Problem 37E

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Chapter 4 Solutions

Beginning and Intermediate Algebra (6th Edition)

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The value of the expression, ( 45 y 7 + 9 y 6 − 6 y 5 + 12 y 4 ) ÷ ( 3 y 8 ) .

Solution Summary: The author calculates the value of a polynomial by dividing each term by the monomial.

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To calculate: The value of the expression, (45y7+9y6−6y5+12y4)÷(3y8).

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Chapter 4 Solutions