Question

Which of the following equations demonstrate that the set of polynomials is not closed under the certain operations?

Answer 1

Do you have the equations? Your question is missing the equations.

Answer 2

Multiplication: (x^2-5x+3)(x-5)=x^3-10x^2+28x-15
Division: (x^2-5x+3) / (x-5)=x+ 3/x-5
Division: (x^2+x)/(x+1)=x
Subtraction: (3x^4 +x^3)-(-2x^4+x^3)=5x

Answer 3

The best answer is "Division: (x^2-5x+3) / (x-5)=x+ 3/x-5"
Note that \((x+3)/(x-5)\) is not a polynomial.

Basically, a set is "closed" under an operation if you do that operation with members of the set and you still get a result that is still in the set.

A polynomial is an algebraic expression with variables and terms; the only operations in a polynomial should be addition, subtraction, multiplication. All variables should have nonnegative integer exponents, i.e. {0,1,2,3,...}. So things such as \(x^2 + 3x + 4\) and \(1 (=x^0)\) and \(3x^2y+5y\) are polynomials but \[ \frac{x^2+3}{4-x}\] is not a polynomial because there is division.

So you can see in that example, doing division got you something that is not a polynomial

Answer 4

Solve x2 u2013 4 = 5 by graphing the related function.

Answer 5

Which statements describe how Antinous is portrayed in this excerpt from Book 21

Answer 6

Let g(x) = 2x and h(x) = x2 + 4.

Evaluate (h u2218 g)(u22122).

Answer 7

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 2x2 + x u2212 3 and g(x) = x u2212 1.

Answer 8

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The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 9

biochem question about molecules @ physiological pH (which is ~7ish)

Answer 10

Math help

Answer 11

Let g(x) = 2x and h(x) = x2 + 4.

Evaluate (h u2218 g)(1).

Answer 12

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 13

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 2x2 + x u2212 3 and g(x) = x + 2.

Answer 14

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 15

Math help

Answer 16

Imagine that you are an adviser to either Chinau2019s emperor or Japanu2019s shogun.

Answer 17

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Answer 18

analytical chem instrumentation question - main difference between a spectrofluor

Answer 19

PLEASE HELP OML!!!!!!!!!!!
1. H2 + Cl2 u2192 HCl (Need to balance equation)
How many grams of HCl can be produced if 7.

Answer 20

The youth group is going on a trip to the state fair. The trip costs $63. Included in that price is $13 for a concert ticket and the cost of 2 passes, one f

Answer 21

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Answer 22

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 23

Let f(x) = 2x2 + x u2212 3 and g(x) = x u2212 1.

Find f(x)/g(x) and state its do