Question

Identify the location of the hole of the following function.

Answer 1

Function:

`g(x)=(x^3-4x^2-19x-14)/(x^2-8x+7)`

Procedure:

0. Factorization of polynomials

`g(x)=(\mleft(x+1\mright)(x-7)(x+2))/(\mleft(x-7\mright)(x-1))`

As we can see, the common factor between the numerator and denominator is (x - 7).

2. Making the common factor equal to zero:

`x-7=0`

3. Solving for x:

`x=7`

Answer: c. There is a hole at x = 7