Find the x and y Intercepts f(x)=(x+5)(x-3)

$f (x) = (x + 5) (x - 3)$

Step 1

Find the x-intercepts.

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

$0 = (x + 5) (x - 3)$

Solve the equation.

Rewrite the equation as $(x + 5) (x - 3) = 0$ .

$(x + 5) (x - 3) = 0$

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

$x + 5 = 0$

$x - 3 = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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.

$x = 3$

The final solution is all the values that make $(x + 5) (x - 3) = 0$ true.

$x = - 5, 3$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0), (3, 0)$

Step 2

Find the y-intercepts.

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

$y = ((0) + 5) ((0) - 3)$

Solve the equation.

Remove parentheses.

$y = (0 + 5) ((0) - 3)$

Remove parentheses.

$y = (0 + 5) (0 - 3)$

Remove parentheses.

$y = ((0) + 5) ((0) - 3)$

Simplify $((0) + 5) ((0) - 3)$ .

Add $0$ and $5$ .

$y = 5 ((0) - 3)$

Subtract $3$ from $0$ .

$y = 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$y = - 15$

y-intercept(s) in point form.

y-intercept(s): $(0, - 15)$

Step 3

List the intersections.

x-intercept(s): $(- 5, 0), (3, 0)$

y-intercept(s): $(0, - 15)$

Step 4

Find the x and y Intercepts f(x)=(x+5)(x-3)

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