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Lelu [443]
3 years ago
12

Use the functions f(x)=7x3−3x2−x+14 f x = 7 x 3 - 3 x 2 - x + 14 and g(x)=2x3+2x+5 g x = 2 x 3 + 2 x + 5 as examples to show tha

t the set of polynomials is closed under subtraction.
Mathematics
1 answer:
Aneli [31]3 years ago
3 0

Answer:

<h3>The given set of polynomials f(x) and g(x) are closed under subtraction.</h3>

Step-by-step explanation:

Given that the functions f ad g are defined by

f(x)=7x^3-3x^2-x+14 and g(x)=2x^3+2x+5 respectively.

<h3>To  show that the set of polynomials is closed under subtraction :</h3>

Now subtract the given polynomials

f(x)-g(x)=(f-g)(x)

=7x^3-3x^2-x+14-(2x^3+2x+5)

=7x^3-3x^2-x+14-2x^3-2x-5

=5x^3-3x^2-3x+9

∴ f(x)-g(x)=5x^3-3x^2-3x+9

  • When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.
<h3>Hence the given polynomials f(x) and g(x) are closed under subtraction.</h3>

∴ f(x)-g(x)=5x^3-3x^2-3x+9 are closed under subtraction,

Hence showed.

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