When we divide polynomials, the easiest case is a polynomial divided by a monomial. This process is done by dividing each term of the polynomial by the monomial. When our divisor is not a monomial, we normally use polynomial long division. This process is very similar to the long division process we use with numbers.

Test Objectives
• Demonstrate the ability to divide a polynomial by a monomial
• Demonstrate the ability to divide a polynomial by another polynomial
• Demonstrate the ability to divide polynomials with missing terms
Dividing Polynomials Practice Test:

#1:

Instructions: Find each quotient.

$$a)\hspace{.2em}\frac{x^4 + 18x^3 + x^2}{6x^2}$$

$$b)\hspace{.2em}\frac{4x^3 + 2x^2 + 16x}{4x}$$

#2:

Instructions: Find each quotient.

$$a)\hspace{.2em}\frac{2x^3 + 5x^2 + 6x}{6x^2}$$

$$b)\hspace{.2em}\frac{x^3 + 9x^2 + 19x - 2}{x + 3}$$

#3:

Instructions: Find each quotient.

$$a)\hspace{.2em}\frac{x^3 + x^2 - 51x - 42}{x - 7}$$

$$b)\hspace{.2em}\frac{56x^2 + 8x^4 - 3 + 56x}{8x + 8}$$

#4:

Instructions: Find each quotient.

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$$a)\hspace{.2em}\frac{x^5 - 3x^4 - 23x^3 - 32x^2 - 18x - 16}{x - 7}$$

$$b)\hspace{.2em}\frac{2x^4 + 10x^3 - 22 - 32x}{4 + 2x}$$

#5:

Instructions: Find each quotient.

$$a)\hspace{.2em}\frac{6x^4 + 3x^3 - 17x^2 - 7x + 7}{3x^2 - 7}$$

$$b)\hspace{.2em}\frac{x^4 - 2x^2 - x - 1}{x^2 - 5}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\frac{x^2}{6}+ 3x + \frac{1}{6}$$

$$b)\hspace{.2em}x^2 + \frac{x}{2}+ 4$$

#2:

Solutions:

$$a)\hspace{.2em}\frac{x}{3}+ \frac{5}{6}+ \frac{1}{x}$$

$$b)\hspace{.2em}x^2 + 6x + 1 - \frac{5}{x + 3}$$

#3:

Solutions:

$$a)\hspace{.2em}x^2 + 8x + 5 - \frac{7}{x - 7}$$

$$b)\hspace{.2em}x^3 - x^2 + 8x - 1 + \frac{5}{8x + 8}$$

#4:

Solutions:

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$$a)\hspace{.2em}x^4 + 4x^3 + 5x^2 + 3x + 3 + \frac{5}{x - 7}$$

$$b)\hspace{.2em}x^3 + 3x^2 - 6x - 4 - \frac{3}{2 + x}$$

#5:

Solutions:

$$a)\hspace{.2em}2x^2 + x - 1$$

$$b)\hspace{.2em}x^2 + 3 + \frac{-x + 14}{x^2 - 5}$$