Question

Can someone please help me factor and write the equations for these two problems ?

Answer 1

Explanation:

Asymptotes 3

g(x) =
`(3x)/(x^2-3x-10)`

Factors of denominator will be,

x² - 3x - 10 = x² - 5x + 2x - 10

= x(x - 5) + 2(x - 5)

= (x + 2)(x - 5)

Therefore, factored form of g(x) will be,

g(x) =
`(3x)/((x + 2)(x - 5))`

Asymptotes 4

h(x) =
`((x-5))/(x^(2) + 14x + 40)`

=
`(x-5)/(x^(2)+10x+4x+40)`

=
`(x-5)/(x(x+10)+4(x+10))`

=
`(x-5)/((x+10)(x+4))`