Question

Identify the location of the hole of the following function.

Answer 1

Function:

$g(x)=\frac{x^3-4x^2-19x-14}{x^2-8x+7}$

Procedure:

0. Factorization of polynomials

$g(x)=\frac{\mleft(x+1\mright)(x-7)(x+2)}{\mleft(x-7\mright)(x-1)}$

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