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