### 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: Find each quotient.

a) (7n^{4} - 43n^{3} - 2n^{2} + 13n + 36) ÷ (7n - 8)

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#2:

Instructions: Find each quotient.

a) (58r - 24r^{2} + 40 + 2r^{3}) ÷ (r - 8)

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#3:

Instructions: Find each quotient.

a) (42x^{4} - 63x^{3} + 3x^{2} + 39x - 14) ÷ (6x - 3)

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#4:

Instructions: Find each quotient.

a) (-32x^{5} - 8x^{4} - 28x^{2} + 72x + 60) ÷ (-8x^{2} + 12)

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#5:

Instructions: Find each quotient.

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) $$-3x^2-2x+5$$