For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$
A) 6, multiplicity 1, crosses x-axis; -7, multiplicity 3, crosses x-axis
B) -6, multiplicity 1, touches x-axis; 7, multiplicity 3
C) -6, multiplicity 1, crosses x-axis; 7, multiplicity 3, crosses x-axis
D) 6, multiplicity 1, touches x-axis; -7, multiplicity 3

Question

Quizplus · Accepted Answer

The polynomial $f(x) = 3(x - 6)(x + 7)^3$ has real zeros at $x = 6$ and $x = -7$. The zero at $x = 6$ has a multiplicity of 1, which means the graph crosses the x-axis at this point. The zero at $x = -7$ has a multiplicity of 3, which is odd, so the graph also crosses the x-axis at this point.

For the Polynomial, List Each Real Zero and Its Multiplicity f(x)=3(x−6)(x+7)3f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }f(x)=3(x−6)(x+7)3

For the Polynomial, List Each Real Zero and Its Multiplicity $f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$