Find the x and y Intercepts f(x)=(x+2)(x+4)(2x+10)

$f (x) = (x + 2) (x + 4) (2 x + 10)$

Step 1

Find the x-intercepts.

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

$0 = (x + 2) (x + 4) (2 x + 10)$

Solve the equation.

Rewrite the equation as $(x + 2) (x + 4) (2 x + 10) = 0$ .

$(x + 2) (x + 4) (2 x + 10) = 0$

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

$x + 2 = 0$

$x + 4 = 0$

$2 x + 10 = 0$

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.

$x = - 2$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set $2 x + 10$ equal to $0$ and solve for $x$ .

Set $2 x + 10$ equal to $0$ .

$2 x + 10 = 0$

Solve $2 x + 10 = 0$ for $x$ .

Subtract $10$ from both sides of the equation.

$2 x = - 10$

Divide each term in $2 x = - 10$ by $2$ and simplify.

Divide each term in $2 x = - 10$ by $2$ .

$\frac{2 x}{2} = \frac{- 10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10}{2}$

Divide $x$ by $1$ .

$x = \frac{- 10}{2}$

Simplify the right side.

Divide $- 10$ by $2$ .

$x = - 5$

The final solution is all the values that make $(x + 2) (x + 4) (2 x + 10) = 0$ true.

$x = - 2, - 4, - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (- 4, 0), (- 5, 0)$

Step 2

Find the y-intercepts.

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

$y = ((0) + 2) ((0) + 4) (2 (0) + 10)$

Solve the equation.

Remove parentheses.

$y = (0 + 2) ((0) + 4) (2 (0) + 10)$

Remove parentheses.

$y = (0 + 2) (0 + 4) (2 (0) + 10)$

Remove parentheses.

$y = ((0) + 2) ((0) + 4) (2 (0) + 10)$

Simplify $((0) + 2) ((0) + 4) (2 (0) + 10)$ .

Add $0$ and $2$ .

$y = 2 ((0) + 4) (2 (0) + 10)$

Add $0$ and $4$ .

$y = 2 \cdot 4 (2 (0) + 10)$

Multiply $2$ by $4$ .

$y = 8 (2 (0) + 10)$

Multiply $2$ by $0$ .

$y = 8 (0 + 10)$

Add $0$ and $10$ .

$y = 8 \cdot 10$

Multiply $8$ by $10$ .

$y = 80$

y-intercept(s) in point form.

y-intercept(s): $(0, 80)$

Step 3

List the intersections.

x-intercept(s): $(- 2, 0), (- 4, 0), (- 5, 0)$

y-intercept(s): $(0, 80)$

Step 4

Find the x and y Intercepts f(x)=(x+2)(x+4)(2x+10)

Related Questions

Support LCMGCF.com by disabling your adblocker.