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Answer :

The results of the division of polynomials are given as follows:

  • h(x) = x + 3 for f(x) = x² - 9 and g(x) = x - 3.
  • h(x) = x + 4 for f(x) = x² - 16 and g(x) = x - 4.
  • h(x) = x - 1 for f(x) = x² - 4x + 3 and g(x) = x - 3.
  • h(x) = x + 5 for f(x) = x² + 4x - 5 and g(x) = x - 1.

What is the division of x² - 9 by x - 3?

Considering that x² - 9 is the subtraction of perfect squares, we have that:

x² - 9 = (x - 3)(x + 3)

Hence the division is:

h(x) = (x - 3)(x + 3)/(x - 3) = x + 3.

What is the division of x² - 16 by x - 4?

Considering that x² - 16 is the subtraction of perfect squares, we have that:

x² - 16 = (x - 4)(x + 4)

Hence the division is:

h(x) = (x - 4)(x + 4)/(x - 4) = x + 4.

What is the division of x² - 4x + 3 by x - 3?

Considering that the roots of x² - 4x + 3 are x = 1 and x = 3, we have that:

x² - 4x + 3 = (x - 1)(x - 3).

Hence the division is:

h(x) = (x - 1)(x - 3)/(x - 3) = x - 1.

What is the division of x² + 4x - 5 by x - 1?

Considering that the roots of x² + 4x - 5 are x = -5 and x = 1, we have that:

x² + 4x - 3 = (x + 5)(x - 1).

Hence the division is:

h(x) = (x + 5)(x - 1)/(x - 1) = x + 5.

More can be learned about division of polynomials at https://brainly.com/question/8433134

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