About Dividing Polynomials with Missing Terms:
Now that we have a general understanding of how to perform polynomial long division, we encounter another obstacle: missing terms. When we are dividing polynomials and discover missing terms, we use "0" as the coefficient for each missing term.
Test Objectives
- Demonstrate the ability to set up a long division with polynomials
- Demonstrate the ability to divide polynomials with missing terms
- Demonstrate the ability to check the result of a polynomial division
#1:
Instructions: Find each quotient.
a) $$(x^3 - 4x^2 + 3) \, ÷ \, (x - 1)$$
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#2:
Instructions: Find each quotient.
a) $$(8x^3 + 61x^2 - 9) \, ÷ \, (8x - 3)$$
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#3:
Instructions: Find each quotient.
a) $$(6p^3 - 43p^2 + 45) \, ÷ \, (6p - 7)$$
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#4:
Instructions: Find each quotient.
a) $$(3x^5 + 5x^4 - 2x^3 - 36x^2 - 60x + 24) \, ÷ \, (x^3 - 12)$$
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#5:
Instructions: Find each quotient.
a) $$(-10x^4 + 6x^3 - 4x^2 + 8x - 2) \, ÷ \, (x^3 - 12)$$
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Written Solutions:
#1:
Solutions:
a) $$x^2 - 3x - 3$$
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#2:
Solutions:
a) $$x^2 + 8x + 3$$
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#3:
Solutions:
a) $$p^2 - 6p - 7 - \frac{4}{6p - 7}$$
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#4:
Solutions:
a) $$3x^2 + 5x - 2$$
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#5:
Solutions:
a) $$-10x + 6 + \frac{-4x^2 - 112x + 70}{x^3 - 12}$$
