Mathematics, 25.08.2019 08:00 jimyyyy

Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

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Answer from: angie249

The correct answer is:

When checking polynomial division, you multiply the quotient by the divisor.

The quotient will be a polynomial (with or without a remainder). Multiplying this polynomial by the polynomial divisor, we get a polynomial in which the exponents and coefficients have changed. Thus polynomials are closed under multiplication.

There will usually be at least two terms in the divisor. When we multiply the quotient by this, we will use the distributive property, multiplying the entire quotient by each term of the divisor. When this process is finished, we will need to add the polynomials we had from multiplying together. Doing this, we get a polynomial answer in which the coefficients have changed. Thus polynomials are closed under addition.

Answer from: avery2020

A polynomial is a finite sum of terms in which all variables have whole number exponents and no variable appears in a denominator.

When adding polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the sum has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under addition.

When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. Remember that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under multiplication.

Answer from: Quest

answer: b.48 for

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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