Find the x and y Intercepts f(x)=(5x+2)^3(x+2)

$f (x) = {(5 x + 2)}^{3} (x + 2)$

Step 1

Find the x-intercepts.

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

$0 = {(5 x + 2)}^{3} (x + 2)$

Solve the equation.

Rewrite the equation as ${(5 x + 2)}^{3} (x + 2) = 0$ .

${(5 x + 2)}^{3} (x + 2) = 0$

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

${(5 x + 2)}^{3} = 0$

$x + 2 = 0$

Set ${(5 x + 2)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(5 x + 2)}^{3}$ equal to $0$ .

${(5 x + 2)}^{3} = 0$

Solve ${(5 x + 2)}^{3} = 0$ for $x$ .

Set the $5 x + 2$ equal to $0$ .

$5 x + 2 = 0$

Solve for $x$ .

Subtract $2$ from both sides of the equation.

$5 x = - 2$

Divide each term in $5 x = - 2$ by $5$ and simplify.

Divide each term in $5 x = - 2$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{5}$

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 ${(5 x + 2)}^{3} (x + 2) = 0$ true.

$x = - \frac{2}{5}, - 2$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{2}{5}, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$y = {(5 (0) + 2)}^{3} ((0) + 2)$

Solve the equation.

Remove parentheses.

$y = {(5 (0) + 2)}^{3} (0 + 2)$

Remove parentheses.

$y = {(5 (0) + 2)}^{3} ((0) + 2)$

Simplify ${(5 (0) + 2)}^{3} ((0) + 2)$ .

Multiply $5$ by $0$ .

$y = {(0 + 2)}^{3} ((0) + 2)$

Add $0$ and $2$ .

$y = 2^{3} ((0) + 2)$

Raise $2$ to the power of $3$ .

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

Add $0$ and $2$ .

$y = 8 \cdot 2$

Multiply $8$ by $2$ .

$y = 16$

y-intercept(s) in point form.

y-intercept(s): $(0, 16)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{2}{5}, 0), (- 2, 0)$

y-intercept(s): $(0, 16)$

Step 4

Find the x and y Intercepts f(x)=(5x+2)^3(x+2)

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