About Polynomial Long Division:
When we divide polynomials, there are two different scenarios. The first and easier of the two involves dividing a polynomial by a monomial. For this type of problem, we set up a fraction and divide each term of the polynomial by the monomial. The second and harder scenario involves dividing polynomials when neither is a monomial. For this type of problem, we generally use polynomial long division.
Test Objectives
- Demonstrate the ability to divide a polynomial by a monomial
- Demonstrate the ability to set up a polynomial long division
- Demonstrate the ability to divide polynomials when remainders are involved
#1:
Instructions: Divide each.
a) $$(7n^4 - 43n^3 - 2n^2 + 13n + 36) \, ÷ \, (7n - 8)$$
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#2:
Instructions: Divide each.
a) $$(58r - 24r^2 + 40 + 2r^3) \, ÷ \, (r - 8)$$
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#3:
Instructions: Divide each.
a) $$(42x^4 - 63x^3 + 3x^2 + 39x - 14) \, ÷ \, (6x - 3)$$
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#4:
Instructions: Divide each.
a) $$(-32x^5 - 8x^4 - 28x^2 + 72x + 60) \, ÷ \, (-8x^2 + 12)$$
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#5:
Instructions: Divide each.
a) $$(-36x^4 - 24x^3 - 40x + 100) \, ÷ \, (12x^2 + 20)$$
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Written Solutions:
#1:
Solutions:
a) $$n^3 - 5n^2 - 6n - 5 + \frac{-4}{7n - 8}$$
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#2:
Solutions:
a) $$2r^2 - 8r - 6 + \frac{-8}{r - 8}$$
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#3:
Solutions:
a) $$7x^3-7x^2-3x+5+\frac{1}{6x-3}$$
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#4:
Solutions:
a) $$4x^3+x^2+6x+5$$
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#5:
Solutions:
a) $$-3x^2-2x+5$$
