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Olegator [25]
3 years ago
15

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

Mathematics
2 answers:
Naddik [55]3 years ago
5 0
<span>Division: (x^2+2x) / (x+1) = x+ x/x+1</span>
lozanna [386]3 years ago
5 0

Solution:

A. Division

  =\frac{x^2+2 x}{x+1}\\\\=\frac{x(x+1)+x}{x+1}\\\\=\frac{x(x+1)}{x+1}+\frac{x}{x+1}\\\\= x+\frac{x}{x+1}

→→→True

B. Multiplication

L HS

(3 x^4+x^3)(-2 x^4+x^3)=3 x^4\times(-2 x^4+x^3)+x^3 \times (-2 x^4+x^3)\\\\=3 \times -2\times x^4 \times x^4 +3 \times 1\times x^4 \times x^3 + x^3 \times x^4 \times -2+x^3 \times x^3\\\\=-6 x^8+3 x^7-2 x^7+x^6\\\\=-6 x^8+ x^7+x^6

R HS

=-6x^6+ x^7+x^6

LHS ≠ RHS

→→→→False

C: Addition

L HS

=(3x^4+x^3)+(-2x^4+x^3)\\\\=3x^4-2x^4+x^3+x^3\\\\ x^4+2 x^3=RHS

→→→True

D: Multiplication

LHS

=(x^2+2 x)(x+1)\\\\= x^2\times(x+1)+2 x\times (x+1)\\\\= x^3+x^2+2 x^2+2 x\\\\= x^3+3x^2+2 x=RHS  

→→→True

Option B: is not correctly closed under Multiplication.

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