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Hellllp meee. How do you add polynomials when you don't have any like terms?
Hellllp meee, how do you add polynomials when you don't have any like terms is a very common questions when it comes to this type of math. However, the polynomials can only be added if all terms are alike. No unlike terms can be added within the polynomials.
What are the rules in addition of polynomials?
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.
Is it possible to add 2 polynomials together and your answer is not a polynomial?
No. Even if the answer is zero, zero is still a polynomial.
When you multiply polynomials what do you do with the exponents?
Add them up providing that the bases are the same.
Rules in adding polynomials?
To add polynomials , simply combine similar terms. Combine similar terms get the sum of the numerical coefficients and affix the same literal coefficient .
How do we add in polynomials?
To add polynomials, align the like terms, which are terms that have the same variable raised to the same power. Then, simply combine the coefficients of these like terms. For example, in the polynomials (3x^2 + 2x + 1) and (4x^2 + 3), you would add (3x^2 + 4x^2) to get (7x^2) and combine the constant terms (1 + 3) to get (4), resulting in (7x^2 + 2x + 4).
Are polynomials a closed set under addition?
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.
How is adding polynomials the same as subtracting polynomials?
just add the negative of the polynomial, that is the same as subtracting it. For example, x^2+2x is a poly, the negative is -x^2-2x. So if we want to subtract x^2+2x from another poly, we can add the negative instead.
What Must the sum of three polynomials again be a polynomial?
The sum of three polynomials must again be a polynomial because polynomials are defined as expressions consisting of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication by constants. When you add polynomials, the resulting expression will still adhere to these rules, maintaining the structure of a polynomial. Specifically, the degrees of the resulting polynomial will be determined by the highest degree among the summed polynomials, ensuring it remains a polynomial. Therefore, the sum of any number of polynomials is always a polynomial.
Polynomials have factors that are?
Other polynomials of the same, or lower, order.
Are polynomials closed under the operations of subtraction addition and multiplication?
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
What are polynomials that have factors called?
Reducible polynomials.
