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Course: Algebra 2 > Unit 1
Lesson 6: Special products of polynomialsPolynomial arithmetic: FAQ
Frequently asked questions about polynomial arithmetic
What is a polynomial?
A polynomial is a type of mathematical expression made up of one or more terms. Each term consists of a variable (usually
Why do we need to know how to add, subtract, and multiply polynomials?
Polynomial arithmetic is important for solving a variety of problems in mathematics, physics, engineering, and more. For example, knowing how to multiply polynomials can help us factor them, which in turn can be useful for solving polynomial equations.
How do we add or subtract two polynomials?
We can add or subtract two polynomials by combining like terms. For example, to add
How do we multiply a monomial by a polynomial?
To multiply a monomial (a polynomial with just one term) by a polynomial, we use the distributive property. For example, to multiply
How do we multiply two binomials?
We can use the distributive property or an area model to multiply two binomials (polynomials with two terms). For example, to multiply
So
What are special products of polynomials?
There are certain polynomial products that occur frequently in mathematics, and it's helpful to recognize them.
For example, the square of a binomial is:
Another common special product is the difference of two squares:
Want to join the conversation?
is it just me that writes the right result on paper and type it wrong?(114 votes)
No, it is not.(18 votes)
I hope that all you beautiful people are having a wonderful day! If you get stressed, remember to breath and try again! I hope everyone has a blessed day!(59 votes)
what is the formola of (a+b)(a-b)(8 votes)- How to combine like terms(9 votes)
- Just learning this but it's basically adding or subtracting terms that have the same variable and degree/exponent. For example adding 3x^2 with 4x^2 is 7x^2. an example with subtraction is 6x^3 with -4x^3 is 2x^3. Some examples of not combining like terms is 9x^3 and 4x^4 due to them having different degrees/exponents. 9x^3 and 10y^3 would not work due to different variables.(8 votes)
- how we can apply polynomial functions in real life application?(5 votes)
Glad you asked! Firstly, tests such as the ACT or SAT may test you on these concepts, as well as concepts that are built off of polynomial functions. By learning about polynomial functions, you can make sure that you get those questions right on your ACT/SAT, which can help you secure a good college.
Even after high school and college, many jobs still require knowledge about polynomial functions. Software engineers, data analysts, and astronomers are all highly desirable positions, and they all require you to know how to utilize polynomial functions, as well as concepts built off of them.
Hope this helps you :)(10 votes)
- What is a polynomial?(4 votes)
A polynomial is a group of numbers with more than one term. 'Poly' meaning many, and 'nomial' referring to the numbers. A binomial is a polynomial, it is just describing that there are two terms, and a trinomial is with 3 terms. Hope that helps(7 votes)
- The answer given in this FAQ to the second question, "Why do we need to know how to add, subtract, and multiply polynomials?", is "so that we can add, subtract, and multiply polynomials.". This is somewhat of a circular answer to a fundamental question about learning polynomials. Couldn't you cite applications of polynomials in academia and industry instead of this seemingly bad answer?(5 votes)
the answer I see in the article is: "Polynomial arithmetic is important for solving a variety of problems in mathematics, physics, engineering, and more. For example, knowing how to multiply polynomials can help us factor them, which in turn can be useful for solving polynomial equations." maybe recheck it?(4 votes)
this is so much fun(6 votes)
Why is it so hard to solve these ?(1 vote)
It just take time to get it. Every one is different when we're learning.(8 votes)
- I am really old-old school, and I learned cross-multiplying but, have noticed that is not taught and I'm sure there's a reason for it?(3 votes)
- Ha..ha! I am 84 years old and have always loved math, so one of my niece's who happens to teach Calculus, referred me to Khan Academy as I just wanted something to keep my mind active as long as possible. My love for math began in my Junior year of high school, after almost flunking two years of Algebra! But, in my Junior year I took Trig and the instructor Mr. George Ahrens(RIP) had only six students compared to 30-40 in the Algebra classes. I give him all the credit in the world for stimulating my interests in math, especially Trig, as he showed us how to measure across a river without crossing it! The same with building a tunnel in one side of a mountain and coming out the other side exactly where one wants to! THAT alone, got my math DNA stirred up! But, now I have been retired from Land and Construction Surveying for over 20 years, and just wanted to try something to keep my mind busy. I am now scared as I am about to take a segment on the Imaginary number which also scared the death outa me over 60 years ago! As you can tell by my record, I seem to do pretty well in a lot of the segments, but others I do not, plus I am horribly slow with some of the problems, especially the Word ones. But, I shall continue and do the best I can. Also, I may want to get into the geometry and coordinate end of math, as I did use coordinate inverses, etc., a lot in my work. In the meantime, thanks so much for what you do for the progress in math learning as it is needed badly in our country....Nate Adams(4 votes)
