### About Synthetic Division:

When we divide a polynomial by a binomial of the form: x - k, we can use a shortcut known as synthetic division. This shortcut allows us to work only with the numerical information and skip dealing with any variables. Once we are done with our process, we can take the numerical information and write our answer.

Test Objectives

- Demonstrate the ability to set up a synthetic division
- Demonstrate the ability to change x + k into x - (-k)
- Demonstrate the ability to write out the answer from a synthetic division

#1:

Instructions: Find each quotient, using synthetic division.

a) (-7k + k^{5} - 13 + 2k^{4}) ÷ (2 + k)

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#2:

Instructions: Find each quotient, using synthetic division.

a) (2 + p^{5} + 4p + 3p^{4}) ÷ (1 + p)

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#3:

Instructions: Find each quotient, using synthetic division.

a) (36 + b^{5} - 9b^{4} + 15b^{3} - 24b + 24b^{2}) ÷ (-4 + b)

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#4:

Instructions: Find each quotient, using synthetic division.

a) (-12v + 2v^{3} + v^{4} - 3 + 5v^{2}) ÷ (v - 1)

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#5:

Instructions: Find each quotient, using synthetic division.

a) (-r^{4} + 5 + 3r - 8r^{2} + r^{5}) ÷ (r - 1)

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Written Solutions:

#1:

Solutions:

a) $$k^4 - 7 + \frac{1}{k + 2}$$

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#2:

Solutions:

a) $$p^4 + 2p^3 - 2p^2 + 2p + 2$$

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#3:

Solutions:

a) $$b^4-5b^3-5b^2+4b-8 + \frac{4}{b - 4}$$

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#4:

Solutions:

a) $$v^3+3v^2+8v-4+\frac{-7}{v-1}$$

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#5:

Solutions:

a) $$r^4-8r-5$$