Yes. Note that specifically, the sum might be a constant (just a number), or even zero, but it is convenient to include those in the definition of "polynomial".
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
No. Even if the answer is zero, zero is still a polynomial.
Clouser
Closure
That property is called CLOSURE.
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
No. Even if the answer is zero, zero is still a polynomial.
It is called the property of "closure".
Yes, the product of two polynomials will always be a polynomial. This is because when you multiply two polynomials, you are essentially combining like terms and following the rules of polynomial multiplication, which results in a new polynomial with coefficients that are the products of the corresponding terms in the original polynomials. Therefore, the product of two polynomials will always be a polynomial.
The property that states the difference of two polynomials is always a polynomial is known as the closure property of polynomials. This property indicates that when you subtract one polynomial from another, the result remains within the set of polynomials. This is because polynomial operations (addition, subtraction, and multiplication) preserve the degree and structure of polynomials. Thus, the difference of any two polynomials will also be a polynomial.
Clouser
Yes. A polynomial multiplying by a polynomial will always have a multi-termed product. Hope this helps!
Closure
That property is called CLOSURE.
Division of one polynomial by another one.
Yes, polynomials are a closed set under addition. This means that if you take any two polynomials and add them together, the result will also be a polynomial. The sum of two polynomials retains the structure of a polynomial, as it still consists of terms with non-negative integer exponents and real (or complex) coefficients.
Let p and q be the two polynomials represented by the linked list. 1. while p and q are not null, repeat step 2. 2. If powers of the two terms ate equal then if the terms do not cancel then insert the sum of the terms into the sum Polynomial Advance p Advance q Else if the power of the first polynomial> power of second Then insert the term from first polynomial into sum polynomial Advance p Else insert the term from second polynomial into sum polynomial Advance q 3. copy the remaining terms from the non empty polynomial into the sum polynomial.