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 set up 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 set up 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
#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) $$\left(\frac{3x^7y^3}{5}-\frac{2x^4y^2}{7}+\frac{2xy}{3}- 3\right) ÷ 4xy^5$$ $$\left(\frac{3x^7y^3}{5}-\frac{2x^4y^2}{7}+\frac{2xy}{3}- 3\right)$$ $$÷\hspace{.5em}4xy^5$$
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#5:
Instructions: Find each quotient.
a) $$\left(\frac{-4x^3y^2}{5}+\frac{8x^2y}{3}- 12x\right) ÷ 20x^9y^7$$ $$\left(\frac{-4x^3y^2}{5}+\frac{8x^2y}{3}- 12x\right)$$ $$÷\hspace{.5em}20x^9y^7$$
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Written Solutions:
#1:
Solutions:
a)
| 4b2 | + | b | + | 4 |
| 2 |
b)
| 3a | - | 1 | + | 3 |
| 3 | a |
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#2:
Solutions:
a)
| 3r3 | - | r2 | + | r |
| 2 |
b)
| 1 | - | 3 | + | 1 |
| 2 | n | n2 |
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#3:
Solutions:
a)
| -x3y | - | 4x2 | + | 2x |
| y |
b)
| 3a2b6 | + | b5 | - | b2 | + | 1 |
| 4 | 4a | 5a2b |
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#4:
Solutions:
a)
| 3x6 | - | x3 | + | 1 | - | 3 |
| 20y2 | 14y3 | 6y4 | 4xy5 |
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#5:
Solutions:
a)
| -1 | + | 2 | - | 3 |
| 25x6y5 | 15x7y6 | 5x8y7 |
