### About Dividing Polynomials by Monomials:

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 Polynomials by Monomials Practice Test:

#1:

Instructions: Find each quotient.

a) (32b3 + 4b2 + 32b) ÷ (8b)

b) (-18a4 + 2a3 - 18a2) ÷ (-6a3)

#2:

Instructions: Find each quotient.

a) (12r5 - 4r4 + 2r3) ÷ (4r2)

b) (-3n3 + 18n2 - 6n) ÷ (-6n3)

#3:

Instructions: Find each quotient.

a) (2x5y3 + 8x4y2 - 4x3y) ÷ (-2x2y2)

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

#4:

Instructions: Find each quotient.

a) $$\left(\frac{3x^7y^3}{5}-\frac{2x^4y^2}{7}+\frac{2xy}{3} - 3\right) ÷ 4xy^5$$ $$\left(\frac{3x^7y^3}{5}-\frac{2x^4y^2}{7}+\frac{2xy}{3} - 3\right)$$ $$÷\hspace{.5em}4xy^5$$

#5:

Instructions: Find each quotient.

a) $$\left(\frac{-4x^3y^2}{5}+\frac{8x^2y}{3}- 12x\right) ÷ 20x^9y^7$$ $$\left(\frac{-4x^3y^2}{5}+\frac{8x^2y}{3}- 12x\right)$$ $$÷\hspace{.5em} 20x^9y^7$$

Written Solutions:

#1:

Solutions:

a)

 4b2 + b + 4 2

b)

 3a - 1 + 3 3 a

#2:

Solutions:

a)

 3r3 - r2 + r 2

b)

 1 - 3 + 1 2 n n2

#3:

Solutions:

a)

 -x3y - 4x2 + 2x y

b)

 3a2b6 + b5 - b2 + 1 4 4a 5a2b

#4:

Solutions:

a)

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

#5:

Solutions:

a)

 -1 + 2 - 3 25x6y5 15x7y6 5x8y7