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### Course: Class 8 (Old)>Unit 8

Lesson 6: Polynomials word problems

# Polynomial word problem: total value of bills

Sal writes a polynomial to express the total value of p twenty dollar bills, q ten dollar bills, and r five dollar bills. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Is there a video on how to graph polynomials?
• you can simplify 20p+10q+5r into 5(4p+2q+r), right?
• Yes. It is a direct application of the distributive law.
• whats the degree of a polynomial and how can i find it?
• The degree of a polynomial is the largest power in the expression. So if we have x^2 + 4x - 21, the degree here would be 2. That would make it a second-degree polynomial. If it was x^3, it would be a third-degree polynomial.
• can a number with an exponent but no variable be a polynomial, such as 5 squared?
• No. 5 squared is not a binomial but 2 squared * 3 is a binomial
(1 vote)
• Would a monomial be a polynomial, because a polynomial has multiple terms and a monomial only has one?
(1 vote)
• Always remember, a monomial IS a polynomial despite the prefix poly- implying that polynomials must have more than one term and mono- implying only one term. I did not know this during a competition and it cost me.
• Is it possible to write p20 (variable first), instead of 20p?
(1 vote)
• Yes, it is possible. p*20 = 20*p due to the commutative property of multiplication. However, the convention is to always write the number then the variable: 20p. This is likely preferred to avoid confusing with other numbers that might follow the variable (like an exponent).
For example: 20p^2. If you put the 20 after the variable, you need to write in a multiplication symbol to ensure clarity.
• what are vertical polynomials and horizantal polynomials?
(1 vote)
• Did you mean vertical and horizontal aymptotes?
(1 vote)
• At the end of the video Sal says that a polynomial is a more general term for more than one term. Is it just a mistake? because in other videos, he says that a monomial (a one-term expression) is also a polynomial, which I tend to disagree with since the suffix 'poly' should mean 'many' and 'mono' is just 'one'
(1 vote)
• A monomial is a polynomial. Monomials are not usually considered polynomials, however. A polynomial has at least one term, for instance even 5 is a monomial.
(1 vote)
• use synthetic division to divide polynomial. (x^2-5x-5x^3+x^4)/(5+x)
(1 vote)
• what is the value of x2 + 2 root 2 + 6
(1 vote)

## Video transcript

Write a polynomial to express the total value of p \$20 bills, q \$10 bills, and r \$5 bills. So what's the value of p \$20 bills? Well if I have p \$20 bills, the value of each of those dollar bills is going to be \$20. So the value all p of them is going to be 20p. If I have one \$20 bill, it's \$20. If I have three \$20 bills, if p is 3, it's going to be \$60. Actually, let me do that in the same color as I underlined it. I underlined it in yellow. So let me do the p \$20 bills. So 20p is the p \$20 bills. Then you have your q \$10 bills. So what's the value of those? Well it's going to be 10q. If I have one \$10 bill, it's worth \$10. If I have ten \$10 bills, if q is 10, this is going to be worth 10 times 10. \$100. And then finally you have your r \$5 bills, which are going to be worth 5r dollars. One \$5 bill, worth \$5. Two \$5 bills, worth \$10. And we're done. We've expressed it as a polynomial. Polynomial just means that we have multiple terms here and this is three terms. We could even call it a trinomial. Polynomial is a more general term for more than one term.