About Dividing Polynomials by Monomials:
Before we get into polynomial long division, we first tackle dividing a polynomial by a monomial. To perform our division, we divide each term of the numerator by the monomial denominator, and simplify the result.
Test Objectives
- Demonstrate the ability to divide a polynomial by a monomial
#1:
Instructions: Find each quotient.
a) $$(32b^3 + 4b^2 + 32b) \, ÷ \, (8b)$$
b) $$(-18a^4 + 2a^3 - 18a^2) \, ÷ \, (-6a^3)$$
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#2:
Instructions: Find each quotient.
a) $$(12r^5 - 4r^4 + 2r^3) \, ÷ \, (4r^2)$$
b) $$(-3n^3 + 18n^2 - 6n) \, ÷ \, (-6n^3)$$
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#3:
Instructions: Find each quotient.
a) $$(2x^5y^3 + 8x^4y^2 - 4x^3y) \, ÷ \, (-2x^2y^2)$$
b) $$(-15a^4b^7 - 20a^2b^6 + 5ab^3 - 4) \, ÷ \, (-20a^2b)$$
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#4:
Instructions: Find each quotient.
a) $$\left(\frac{3x^7y^3}{5}-\frac{2x^4y^2}{7}+\frac{2xy}{3}- 3\right) \, ÷ \, 4xy^5$$
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#5:
Instructions: Find each quotient.
a) $$\left(\frac{-4x^3y^2}{5}+\frac{8x^2y}{3}- 12x\right) \, ÷ \, 20x^9y^7$$
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Written Solutions:
#1:
Solutions:
a) $$4b^2 + \frac{b}{2} + 4$$
b) $$3a - \frac{1}{3} + \frac{3}{a}$$
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#2:
Solutions:
a) $$3r^3 - r^2 + \frac{r}{2}$$
b) $$\frac{1}{2} - \frac{3}{n} + \frac{1}{n^2}$$
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#3:
Solutions:
a) $$-x^3y - 4x^2 + \frac{2x}{y}$$
b) $$\frac{3a^2b^6}{4} + b^5 - \frac{b^2}{4a} + \frac{1}{5a^2b}$$
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#4:
Solutions:
a) $$\frac{3x^6}{20y^2} - \frac{x^3}{14y^3} + \frac{1}{6y^4} - \frac{3}{4xy^5}$$
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#5:
Solutions:
a) $$-\frac{1}{25x^6y^5} + \frac{2}{15x^7y^6} - \frac{3}{5x^8y^7}$$
