Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .
A)x-intercept: none;y-intercept: none
B)x-intercept: $\left( - \frac { 7 } { 5 } , 0 \right)$ ;y-intercept: none
C)x-intercept: (-2,0);y-intercept: (0,-2)
D)x-intercepts: (-5,0), (-1,0), (1,0);y-intercept: (0,-2)
E)x-intercept: (0,0);y-intercept: (0,0)

Question

Quizplus · Accepted Answer

To find the x-intercepts, set $f(x) = 0$ and solve for $x$. Factoring the numerator gives $(x+5)(x+2)$, and factoring the denominator gives $(x+5)(x^2-x-1)$. The x-intercept is at $x = -2$, since $x = -5$ is a hole (not an intercept) due to it being a factor in both the numerator and denominator.To find the y-intercept, set $x = 0$ in $f(x)$, which gives $f(0) = \frac{10}{-5} = -2$. Thus, the y-intercept is $(0, -2)$.

Identify All Intercepts Of f(x)=x2+7x+10x3+5x2−x−5f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }f(x)=x3+5x2−x−5x2+7x+10​

Identify All Intercepts Of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$