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Why it is not possible to add two polynomials of degree 3 and get a polynomial of 4?
When you add polynomials, you simply add the coefficients of the variable taken to the same degree. For example
(x3 + 2x2 + 3x + 4) added to (2x3 - 4x2 + x -2) would give you
[(1+2)x3 + (2-4)x2 + (3+1)x + (4-2)] or
3x3 - 2x2 + 4x + 2
You would get a fourth degree polynomial by multiplying this one by x.
Another way to think of it: If you add 1 apple and 3 apples (like one times x2 and 3 times x2) you still get apples, not watermelons.
What else can I help you with?
Can two third-degree polynomials be added to produce a second-degree polynomial?
Yes. If the coefficient of the third degree terms in one polynomial are the additive inverses (minus numbers) of the coefficient of the corresponding terms in the second polynomial. Eg: 3x3 + 2x2 + 5 and -3x3 + x - 7 add to give 2x2 + x - 2
Multiplication of polynomial by a polynomial?
Distribute... You have to make sure you multiply each term by each term and the only way is to distribute. don't really know of any other way. Remember to add all of the like terms first so you dont have to do extra work.
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Why would you want to rename fractions with the LCD?
Possible reasons: To add or subtract fractions, To compare fractions with different denominators.
What is the temperature in Fahrenheit if it is 32.3 degrees celsius?
Start by multiplying 32.3 with 9 and divide by 5. Then add 32 to the answer. In this case the answer is 90.14 degree Fahrenheit .
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.
Is 4 - 3x plus 5x2 a polynomial?
Yes. If you add, subtract or multiply (but not if you divide) any two polynomials, you will get a polynomial.
Can two third-degree polynomials be added to produce a second-degree polynomial?
Yes. If the coefficient of the third degree terms in one polynomial are the additive inverses (minus numbers) of the coefficient of the corresponding terms in the second polynomial. Eg: 3x3 + 2x2 + 5 and -3x3 + x - 7 add to give 2x2 + x - 2
How do explain how to multiply polynomials?
You simply need to multiply EACH term in one polynomial by EACH term in the other polynomial, and add everything together.
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.
What is the degree an algebraic ezpression?
The "degree" is only specified for polynomials. The degree of a monomial (a single term) is the sum of the powers of all the variables. For example, x3y2z would have the degree 6; you have to add 3 + 2 + 1 (since z is the same as z to the power 1). The degree of a polynomial is the degree of its highest monomial.
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.
Can there be two patterns in a sequence?
Yes, there can be infinitely many. Given a sequence of n numbers, it is always possible to fit a polynomial of degree (n-1) to it. That polynomial is one posible pattern.Then suppose the sequence is extended by adding an (n+1)thnumber = k. You now have a sequence of n+1 numbers and there is a polynomial of degree n that will fit it. For each of an infinite number of values of k, there will be a different polynomial of degree n. Next add another number, l. There will now be an infinite number of polynomials of degree n+1. And this process can continue without end.And these are only polynomial functions. You can have other rules - for example, sums of sines and cosines (see Fourier transformations if you are really keen and able).
What operations are polynomials closed under?
+,-,X only
How do you add polynomials with dissimilar terms?
To add polynomials with dissimilar terms, you simply combine like terms by collecting the terms with the same variables and exponents. If a variable or exponent is not present in one polynomial, you leave it as it is. Then, you can add or subtract the coefficients of the like terms to arrive at your final answer.
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 is the polynomial degree of 4ab5 2ab-3a4b3?
To find the polynomial degree you have only to add the exponents of all of the different components of the polynomial. In your case, you would add 1 and 5 from 4ab5 to get 6, 1 and 1 from 2ab to get 2, and 4 and 3 from 3a4b3 to get 7. Since the degree of the third component is the highest, that is you're answer.
