Question

Help would be appreciated.

Answer 1

Explanation:

1). f(x) = x² - 9

g(x) = x - 3

h(x) = f(x) ÷ g(x)

=

=

= (x + 3)

2). f(x) = x² - 4x + 3

= x² - 3x - x + 3

= x(x - 3) - 1(x - 3)

= (x - 1)( x- 3)

g(x) = x - 3

h(x) = f(x) ÷ g(x)

=

= (x - 1)

3). f(x) = x² + 4x - 5

= x² + 5x - x - 5

= x(x + 5) - 1(x + 5)

= (x - 1)(x + 5)

g(x) = x - 1

h(x) = f(x) ÷ g(x)

=

= (x + 5)

4). f(x) = x² - 16

= (x - 4)(x + 4) [Since a² - b² = (a - b)(a + b)]

g(x) = (x - 4)

h(x) = f(x) ÷ g(x)

=

= (x + 4)

Answer 2

Explanation:

1). f(x) = x² - 9

g(x) = x - 3

h(x) = f(x) ÷ g(x)

=
`(x^2-9)/(x-3)`

=
`((x+3)(x-3))/((x-3))`

= (x + 3)

2). f(x) = x² - 4x + 3

= x² - 3x - x + 3

= x(x - 3) - 1(x - 3)

= (x - 1)( x- 3)

g(x) = x - 3

h(x) = f(x) ÷ g(x)

=
`((x-1)(x-3))/((x-3))`

= (x - 1)

3). f(x) = x² + 4x - 5

= x² + 5x - x - 5

= x(x + 5) - 1(x + 5)

= (x - 1)(x + 5)

g(x) = x - 1

h(x) = f(x) ÷ g(x)

=
`((x-1)(x+5))/((x-1))`

= (x + 5)

4). f(x) = x² - 16

= (x - 4)(x + 4) [Since a² - b² = (a - b)(a + b)]

g(x) = (x - 4)

h(x) = f(x) ÷ g(x)

=
`((x-4)(x+4))/((x-4))`

= (x + 4)