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.
Yes. If you add, subtract or multiply (but not if you divide) any two polynomials, you will get a polynomial.
evaluating polynomials
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.
put the variable that has the highest degree first.
Other polynomials of the same, or lower, order.
You need to find the common denominator in order to add or subtract them. You can only add or subtract "like things" and by finding a common denominator you make both rational expressions into things that can be added or subtracted.
Yes. If you add, subtract or multiply (but not if you divide) any two polynomials, you will get a polynomial.
descending
You subtract a polynomial by adding its additive inverse. For example, subtracting (x - y) is the same as adding (-x + y). Alternately, you can simply subtract similar terms - that is, subtract the coefficients (the numbers) for terms that have the same combination of variables.
evaluating polynomials
+,-,X only
descending form
475
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.
before and after use an conpair the results
Reducible polynomials.