Dividing Polynomials with Long Division

Dividing Polynomials with Long Division

by Tanner Howell

Multiple Choice

Dividing polynomials requires that your dividend be written both in standard form and such that no variable is missing between the largest and smallest exponent (in descending order). You must insert placeholders (zeroes) if a term(s) is missing in your dividend. Does the polynomial $$4x^2+23x-16$$  require any placeholders?

• No

• Yes

• There is not enough information.

Now that you have confirmed that your dividend is written correctly, consider what your next step should be and answer the following question.

Multiple Choice

What step should you take to begin this problem.

• Divide 23x by x and write "23" above 23x. 

• Divide  $$4x^2$$  by x and write 4x above 23x.

• Divide  $$4x^2$$  and 23x by x and then write your answer in order above the dividend.

• Multiply -16 by x and 5 and subtract your answer from the dividend. 

Multiple Choice

After dividing $$4x^2$$  by x and writing 4x above 23x, what is the next step that you should take in solving this problem?

• Divide 23x by x and write 23 above -16.

• Multiply 4x by x and write $$4x^2$$  beneath $$4x^2$$  .

• Multiply 4x by x and 5, then write $$4x^2+20$$    beneath $$4x^2+23x$$  .

• Multiply 4x by x and 5, then write $$4x^2+20$$    beneath $$4x^2+23$$  .

Multiple Choice

The next step you should take is to "subtract." What difference will you find?

• $$0x^2+3x$$  

• $$8x^2+43x$$  

• $$8x^2+3x$$  

• $$0x^2-3x$$  

Multiple Choice

Which selection is the final answer?

• $$4x+3-31$$  

• $$4x-28$$  

• $$4x+3-\frac{31}{4x+3}$$  

• $$4x+3-\frac{31}{x+5}$$  

​This is a separate example for you to view. Notice that the remainder is written a bit differently in this problem.

Multiple Choice

Consider the given polynomial $$x^2+3$$  . Does the polynomial require placeholders before long division can be performed? If yes, pick the correct placeholder.

• No

• Yes, 0x should be included.

• Yes, $$0x^3$$  should be included.

• Yes, $$0x^2$$  should be included.

Multiple Choice

Perform the given division problem. What is your final answer? Take your time, and show your work.

• $$x+1+\frac{4}{x-1}$$  

• $$x-1-\frac{4}{x-1}$$  

• $$x+1-\frac{4}{x+1}$$  

• $$x+1+\frac{3}{x-1}$$