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Polynomial/Monomial Test
About Dividing a Polynomial by a Monomial:

When we divide with polynomials, we begin with the simplest process: dividing a polynomial by a monomial. To divide a polynomial by a monomial, we setup the problem as a fraction. Next, we divide each term of the numerator by the denominator and report our answer.

Test Objectives:

•Demonstrate the ability to setup the division of a polynomial by a monomial in fractional form

•Demonstrate the ability to divide a polynomial by a monomial

•Demonstrate the ability to check the result of a polynomial division

Dividing a Polynomial by a Monomial Test:




#1:


Instructions: Find each quotient.


a) (32b3 + 4b2 + 32b) ÷ (8b)


b) (-18a4 + 2a3 - 18a2) ÷ (-6a3)


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#2:


Instructions: Find each quotient.


a) (12r5 - 4r4 + 2r3) ÷ (4r2)


b) (-3n3 + 18n2 - 6n) ÷ (-6n3)


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#3:


Instructions: Find each quotient.


a) (2x5y3 + 8x4y2 - 4x3y) ÷ (-2x2y2)


b) (-15a4b7 - 20a2b6 + 5ab3 - 4) ÷ (-20a2b)


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#4:


Instructions: Find each quotient.


a)


( 3x7y3  -  2x4y2  +  2xy  -  3 )  ÷  4xy5
   5    7   3

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#5:


Instructions: Find each quotient.


a)


( -4x3y2  +  8x2y  -  12x )  ÷  20x9y7
5 3

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Written Solutions:




#1:


Solution:


a)


4b2  +  b  +  4
2

b)


3a  -  1  +  3
3 a

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#2:


Solution:


a)


3r3  -  r2  +  r
2

b)


1  -  3  +  1
2 n n2

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#3:


Solution:


a)


-x3y  -  4x2  +  2x
 y

b)


3a2b6  +  b5  -  b2  +  1
4 4a 5a2b

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#4:


Solution:


a)


3x6  -  x3  +  1  -  3
20y2 14y3 6y4 4xy5

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#5:


Solution:


a)


-1  +  2  -  3
25x6y5 15x7y6 5x8y7

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