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Algebra (all content)
Course: Algebra (all content) > Unit 10
Lesson 9: Polynomials word problemsPolynomial 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.
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Is there a video on how to graph polynomials?(7 votes)
you can simplify 20p+10q+5r into 5(4p+2q+r), right?(4 votes)
Yes. It is a direct application of the distributive law.(4 votes)
whats the degree of a polynomial and how can i find it?(2 votes)
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.(3 votes)
can a number with an exponent but no variable be a polynomial, such as 5 squared?(2 votes)
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.(2 votes)
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.(2 votes)
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.