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Add 3x4 - 7x3 + 12x - 9
GUEST, GUEST
to
The sum is closed because
Roxanne wants to test the idea
that polynomials are closed
under addition. Her work and
explanation are shown.
are
and by definition
the sum is a polynomial.
Drag an expression and phrases
to the boxes to complete the
statement.
5x2 - (2x)3 + (4x)-1
(2x)3 + 2.1x2 - 11
-8x-2 f(3x)3 - 12x6 + 7
the exponents
the variables
the coefficients
integers
whole numbers
real numbers

Add 3x4 7x3 12x 9 GUEST GUEST To The Sum Is Closed Because Roxanne Wants To Test The Idea That Polynomials Are Closed Under Addition Her Work And Explanation Ar class=

Sagot :

MrRoyal

The complete statements are:

  • Add [tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] to [tex]\mathbf{(2x)^3 +2.1x^2-11}[/tex].
  • The sum is closed because the exponents are whole numbers,
  • And by definition, the sum is a polynomial

The polynomial is given as:

[tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex]

Polynomials are closed under addition.

This means that, when the polynomial is added to another, the exponents do not change.

The above highlight mean that:

[tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] cannot be added to [tex]\mathbf{5x^2 -(2x)^3 + (4x)^{-1}}[/tex] and [tex]\mathbf{-8x^{-2} +(3x)^3 -12x^6+ 7}[/tex], because they are not polynomials, and they have negative exponents

However, [tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] can be added to [tex]\mathbf{(2x)^3 +2.1x^2-11}[/tex]

The sum will give:

[tex]\mathbf{3x^4 -7x^3 + 12x - 9 + (2x)^3 +2.1x^2-11 = 3x^4 + x^3+2.1x^2 + 12x - 20}[/tex]

Read more about closure of polynomials at:

https://brainly.com/question/11391029

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