Question

how many different roots does the polynomial function have y = (x-2)(x+3)^2 have

Answer 1

Answer:

$x=2,-3$

Step-by-step explanation:

Set $(x-2)(x+3)^2$ equal to $0$.

$(x-2)(x-3)^22=0$

Solve for $x$.

If any individual factor on the left side of the equation is equal to $0$, the entire expression will be equal to $0$.

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

Set the first factor equal to $0$ and solve.

Set the first factor equal to $0$.

$x-2=0$

Add $2$ to both sides of the equation.

$x=2$

Set the next factor equal to $0$ and solve.

Set the next factor equal to $0$.

$(x+3)^2=0$

Set the $x+3$ equal to $0.$

$x+3=0$

Subtract $-3$ from both sides of the equation.

$x=-3$

The final solution is all the values that make $(x-2)(x+3)^2=0$ true.

$x=2,-3$