Answer:
Step-by-step explanation:
1). f(x) = x² - 9
g(x) = x - 3
h(x) = f(x) ÷ g(x)
= [tex]\frac{x^2-9}{x-3}[/tex]
= [tex]\frac{(x+3)(x-3)}{(x-3)}[/tex]
= (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)
= [tex]\frac{(x-1)(x-3)}{(x-3)}[/tex]
= (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)
= [tex]\frac{(x-1)(x+5)}{(x-1)}[/tex]
= (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)
= [tex]\frac{(x-4)(x+4)}{(x-4)}[/tex]
= (x + 4)
