Find the x and y Intercepts F(x)=(x-3)(x+2)

$F (x) = (x - 3) (x + 2)$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

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

Solve the equation.

Rewrite the equation as $(x - 3) (x + 2) = 0$ .

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

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

$x - 3 = 0$

$x + 2 = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

$x = 3, - 2$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = ((0) - 3) ((0) + 2)$

Solve the equation.

Remove parentheses.

$y = (0 - 3) ((0) + 2)$

Remove parentheses.

$y = (0 - 3) (0 + 2)$

Remove parentheses.

$y = ((0) - 3) ((0) + 2)$

Simplify $((0) - 3) ((0) + 2)$ .

Subtract $3$ from $0$ .

$y = - 3 ((0) + 2)$

Add $0$ and $2$ .

$y = - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 2, 0)$

y-intercept(s): $(0, - 6)$

Step 4

Find the x and y Intercepts F(x)=(x-3)(x+2)

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