at which root does the graph of $f(x)=(x + 4)^6(x + 7)^5$ cross the $x$-axis?\n-7\n-4\n4\n7

Answer:

A. -7

Explanation:

Step1: Recall root - crossing rule

A graph of $y = f(x)$ crosses the $x$-axis at a root $x = a$ if the multiplicity of the factor $(x - a)$ is odd.

Step2: Analyze multiplicities

For $f(x)=(x + 4)^{6}(x + 7)^{5}$, the factor $(x + 4)$ has multiplicity 6 (even), and the factor $(x + 7)$ has multiplicity 5 (odd).

Step3: Find the root

Set $x+7 = 0$, we get $x=-7$. So the graph crosses the $x$-axis at $x=-7$.