Sign In
Ask Question
Gabriella Perez
Mathematics
16 March, 19:14
5r^2s^3 as a monomial
+3
Answers (
1
)
Kenneth Noble
16 March, 19:19
0
A monomial is an expression in algebra that contains one term, like 3xy. Monomialsinclude: numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together.
Identifying a Monomial
Any number, all by itself, is a monomial, like 5 or 2700. A monomial can also be a variable, like "m" or "b". It can also be a combination of these, like 98b or 78xyz. It cannot have a fractional or negative exponent. These are not monomials: 45x+3, 10 - 2a, or 67a - 19b + c.
Two rules about monomials are:
A monomial multiplied by a monomial is also a monomial. A monomial multiplied by a constant is also a monomial.
When looking at examples of monomials, you need to understand different kinds of polynomials. Following is an explanation of polynomials, binomials, trinomials, and degrees of a polynomial.
Polynomials
A polynomial is an algebraic expression with a finite number of terms. These terms are in the form "axn" where "a" is a real number, "x" means to multiply, and "n" is a non-negative integer. Examples are 7a2 + 18a - 2, 4m2, 2x5 + 17x3 - 9x + 93, 5a-12, and 1273.
Binomials
A binomial is a polynomial with two terms. 3x + 1, 2x3 - 5x, x4 - 4, x - 19 are examples of binomials.
Trinomials
A trinomial is a polynomial with three terms. Examples of trinomials are 2x2 + 4x - 11, 4x3 - 13x + 9, 7x3 - 22x2 + 24x, and 5x6 - 17x2 + 97.
Degrees of Polynomials
The degree of a polynomial is the highest power of the variable in that polynomial, as long as there is only one variable. The degree of the polynomial 7x3 - 4x2 + 2x + 9 is 3, because the highest power of the variable "x" is 3. In 18s12 - 41s5 + 27, the degree is 12. The degree of this polynomial 8z + 2008 is 1, because "z" is in the first power.
If a polynomial has more than one variable, then the degree of that monomial is the sum of the exponents of those variables. In this polynomial, 24xyz, the degree is 3 because the sum of degrees of x, y and z is 1 + 1 + 1 = 3. The degree of this polynomial 12x4y2z7 is 13 because 4 + 2 + 7 = 13. 14x3 + 27xy - y has the degree of 6 because 3 + 1 + 1 + 1 + = 6. So basically, you add all the exponents together.
Algebra Terms
When looking at examples of monomials, binomials, and trinomials, it can seem a little confusing at first. It is just a classification for different polynomials with different numbers of terms. A second degree polynomial is also called a "quadratic." Examples are 4x2, x2 - 9, or 6x2 + 13x + c. Just for fun, a third degree polynomial is called a "cubic", a fourth degree is called a "quartic", and a fifth degree polynomial is called a "quintic.
You may wonder where the word "quadriatic" comes from, because the prefix "quad" usually stands for four. The word comes from the Latin word for "making square." So, in this instance, "quad" refers to the four corners of a square, like when you multiply six feet by six feet, you get 36 square feet.
History of Algebra
Algebra is a branch of pure mathematics. Pure mathematics differs from other disciplines because it is not necessarily applied to any particular situation but the concepts and beauty of math is investigated. The Greeks created geometric algebra, representing sides of objects with lines and letters. In the 3rd century AD, Diophantus, who is called the "father of algebra", wrote several books called Arithmetica. In them, he explained how to solve algebraic equations.
The word "algebra" actually comes from Arabic and means "restoration." Algebra actually started with the Babylonians, who were advanced mathematicians, dealing with quadratic and linear equations. Other civilizations at this time were still solving problems geometrically.
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“5r^2s^3 as a monomial ...”
in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
Write 47 and 1000 as a decimal
Answers (1)
Solve for x. 6 (x - 1) = 9 (x + 2) O x=-8 O X=-3 O x=3 Ox=8
Answers (2)
What happens to the average kinetic energy of water molecules as water freezes? A. It decreases as the water releases energy to its surroundings. B. It increases as the water releases energy to its surroundings. C.
Answers (1)
A shirt originally cost $47.26, but it is on sale for $44.90. What is the percentage decrease of the price of the shirt?
Answers (2)
Identify each number as prime or composite. If the number is composite, list all of its factors.
Answers (1)
New Questions in Mathematics
Wath is 346 rounded to the nearest hundred
Answers (1)
Twana thomas is paid $10.50 an hour for a regular 40-hour week. She earns time and a half if she works overtime. This week Thomas worked her regular 40 hours plus 8 1/2 hours of overtime. What is her total pay? A. $456.00 B. $420.00 C. $553.88 D.
Answers (1)
in 10 words or fewer, describe what happens to the symbol when you multiply or divide each side of an inequality by a negative number
Answers (2)
The ratio of boys to girls in Janice's classroom is 3:5, and there are a total of 32 students in the class. Using complete sentences, explain how you could draw a tape diagram to represent this situation.
Answers (1)
Describe the difference between sociology and psychology
Answers (1)
Home
»
Mathematics
» 5r^2s^3 as a monomial
Sign In
Sign Up
Forgot Password?