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madam [21]
4 years ago
14

Which set is closed under subtraction?

Mathematics
2 answers:
AURORKA [14]4 years ago
8 0
The set that is closed under subtraction is rational numbers
Marrrta [24]4 years ago
5 0

Answer:

The correct answer is rational numbers.

Step-by-step explanation:

We consider that a set is closed when the two elements that are part of an operation result in an element belonging to the same group.

As for rational numbers, they are all those that can be represented as the quotient of two whole numbers or, a whole and a positive natural.

These types of numbers are considered in a set closed under addition, subtraction, and multiplication.

Given this information we can say that the correct answer is rational numbers.

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Factor the expression completely over the complex numbers.
nekit [7.7K]

Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

x^3-4x^2+4x-16

It can be written as

f(x)=x^3-4x^2+4x-16

According to the rational root theorem, all possible rational roots are in the form of

\frac{a_0}{a_n}

Where, a₀ is constant term and a_n is leading coefficient.

f(4)=4^3-4(4)^2+4(4)-16=0

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

(x^3-4x^2+4x-16)=(x-4)(x^2+4)

(x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)

(x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

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4 years ago
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