Algebra Examples

$f (x) = (3 x - 5) (x + 9)$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = (3 x - 5) (x + 9)$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $(3 x - 5) (x + 9) = 0$ .

$(3 x - 5) (x + 9) = 0$

Step 1.2.2

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

$3 x - 5 = 0$

$x + 9 = 0$

Step 1.2.3

Set $3 x - 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 1.2.3.1

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Step 1.2.3.2

Solve $3 x - 5 = 0$ for $x$ .

Tap for more steps...

Step 1.2.3.2.1

Add $5$ to both sides of the equation.

$3 x = 5$

Step 1.2.3.2.2

Divide each term in $3 x = 5$ by $3$ and simplify.

Tap for more steps...

Step 1.2.3.2.2.1

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Step 1.2.3.2.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.3.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.3.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Step 1.2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 1.2.4

Set $x + 9$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 1.2.4.1

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Step 1.2.4.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 1.2.5

The final solution is all the values that make $(3 x - 5) (x + 9) = 0$ true.

$x = \frac{5}{3}, - 9$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{3}, 0), (- 9, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = (3 (0) - 5) ((0) + 9)$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = (3 (0) - 5) (0 + 9)$

Step 2.2.2

Remove parentheses.

$y = (3 (0) - 5) ((0) + 9)$

Step 2.2.3

Simplify $(3 (0) - 5) ((0) + 9)$ .

Tap for more steps...

Step 2.2.3.1

Multiply $3$ by $0$ .

$y = (0 - 5) ((0) + 9)$

Step 2.2.3.2

Subtract $5$ from $0$ .

$y = - 5 ((0) + 9)$

Step 2.2.3.3

Add $0$ and $9$ .

$y = - 5 \cdot 9$

Step 2.2.3.4

Multiply $- 5$ by $9$ .

$y = - 45$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 45)$

Step 3

List the intersections.

x-intercept(s): $(\frac{5}{3}, 0), (- 9, 0)$

y-intercept(s): $(0, - 45)$

Step 4