If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 2>Unit 4

Lesson 3: Dividing polynomials by linear factors

# Dividing polynomials by linear expressions: missing term

This lesson guides you through the process of dividing polynomials by linear factors, showing you how to neatly organize your work and avoid common errors. You'll learn how to handle missing degree terms and ensure correct subtraction. The result? You'll confidently simplify and rewrite complex rational expressions.

## Want to join the conversation?

• What is "The Price is Right"?
• “The Price is Right” is a game show with different pricing games that rewards contestants for knowledge of prices of goods.
• How do you constrain the domain? Do you need to know how to?
• you need to, yes, and to do so you just need to know what the domain of functions are.

For instance if a function has a square root, you know the things under the square root cannot be less than 0. Logs cannot be 0 or less, and so on.

So a kinda complex example that will show what to do is something like sqrt(ln(1/(x-1)))

So you have the square root of the natural log of 1/(x-1) so let's take it one step at a time.

square root has to be 0 or greater, so the domain is 0 to infinity.

natural log has to just be greater than 0, so not the domain changes to be greater just greater than 0, this is because this has both square root and a log.

the last part is 1/(x-1) for functions with a variable int he denominator of a fraction, the denominator cannot be 0. so when does x-1=0? you just use some algebra, xo it is 0 when x = 1.

Now the domain changes again to be greater than 0 except for the value 1.

Let me know if that doesn't help.
• what if your trying to divide a polynomial has a cube and than a square and than a regular number. what do u insert for the missing term?
• A third-degree polynomial would look like this:
𝑎𝑥³ + 𝑏𝑥² + 𝑐𝑥 + 𝑑

However, in our case the 𝑥-term is missing, so we would replace 𝑐 with 0.
• I dont understand this format p(x)+k/x+1 that is asked in practices exercises​
• p(x)+k/x+1
The main thing to worry about is the denominator, as x=-1 is the vertical asymptote. Formatting wise,

p(x) is any polynomial
k is any constant term
hopefully that helps !
• At , why did Sal add "0x^2" between "2x^3" and "-47x" in the expression "2x^3 - 47x - 15"?
• It leaves the spot needed to divide the number. It would be comparable to regular division such as 305/5, without the 0 it would get an incorrect answer.
• I'm struggling with how I would write the integers of the final polynomial. For example, when I did this question, I thought it was -10x not +10x in the answer. It would help if i had a rule for the integers..?
• There is a rule :D

First, let me explain how negatives and positives work. Note that I use multiplication and division in the example because it may make more sense, but this also applies to addition and subtraction.
Key:
+ = positive
- = negative
★ A + number multiplied or divided by a + number is positive (you probably knew that).
★ A - number multiplied or divided by a + number is negative.
★ A - number multiplied or divided by a - number is +.

This may seem confusing or hard to remember at first, but there is a cool way of remembering this!

+ = friend
- = enemy
★ A friend of a friend is your friend.
Translates to: + times + = +.
Translates to: - times + = -.
Translates to: - times - = +.

Kind of makes sense if you think about it, right? That's how positives and negatives work!
- - -
In your example from the video, Sal got +10x^2 because he was subtracting a negative number from 0x^2. Subtracting a negative number translates to: 10x^2-(-10x^2)= 10x^2.

Hopefully that helps :). I'm not the best at explaining things, so if you would like me to clarify anything, please ask!
• What is prices right?
(1 vote)
• Do you have to write 0x^2 or keep it blank?
• I would strongly suggest adding 0x^2, as doing the division without it can be messy and easier to make a mistake on.