Question

find the zeros for the polynomial function and give the multiplicity for each zero. state whether the graph crosses the x - axis or touches the x - axis and turns around at each f(x)=-4(x + 3)(x + 4)^2 determine the zero(s). the zero(s) is/are . (type integers or decimals. use a comma to separate answers as needed.)

Explanation:

Step1: Set the function equal to zero

$-4(x + 3)(x + 4)^2=0$

Step2: Use the zero - product property

If $ab = 0$, then $a = 0$ or $b = 0$. So $x+3=0$ or $(x + 4)^2=0$.

Step3: Solve for $x$ in $x+3=0$

$x=-3$

Step4: Solve for $x$ in $(x + 4)^2=0$

Taking the square - root of both sides, $x+4 = 0$, so $x=-4$

Answer:

$-3,-4$