Find the x and y Intercepts f(x)=(x+3)^3(5x-1)^3

$f (x) = {(x + 3)}^{3} {(5 x - 1)}^{3}$

Step 1

Find the x-intercepts.

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

$0 = {(x + 3)}^{3} {(5 x - 1)}^{3}$

Solve the equation.

Rewrite the equation as ${(x + 3)}^{3} {(5 x - 1)}^{3} = 0$ .

${(x + 3)}^{3} {(5 x - 1)}^{3} = 0$

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

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

${(5 x - 1)}^{3} = 0$

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

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

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

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

Set the $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set ${(5 x - 1)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(5 x - 1)}^{3}$ equal to $0$ .

${(5 x - 1)}^{3} = 0$

Solve ${(5 x - 1)}^{3} = 0$ for $x$ .

Set the $5 x - 1$ equal to $0$ .

$5 x - 1 = 0$

Solve for $x$ .

Add $1$ to both sides of the equation.

$5 x = 1$

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Divide $x$ by $1$ .

$x = \frac{1}{5}$

The final solution is all the values that make ${(x + 3)}^{3} {(5 x - 1)}^{3} = 0$ true.

$x = - 3, \frac{1}{5}$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0), (\frac{1}{5}, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) + 3)}^{3} {(5 (0) - 1)}^{3}$

Solve the equation.

Remove parentheses.

$y = {(0 + 3)}^{3} {(5 (0) - 1)}^{3}$

Remove parentheses.

$y = {((0) + 3)}^{3} {(5 (0) - 1)}^{3}$

Simplify ${((0) + 3)}^{3} {(5 (0) - 1)}^{3}$ .

Add $0$ and $3$ .

$y = 3^{3} {(5 (0) - 1)}^{3}$

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

$y = 27 {(5 (0) - 1)}^{3}$

Multiply $5$ by $0$ .

$y = 27 {(0 - 1)}^{3}$

Subtract $1$ from $0$ .

$y = 27 {(- 1)}^{3}$

Raise $- 1$ to the power of $3$ .

$y = 27 \cdot - 1$

Multiply $27$ by $- 1$ .

$y = - 27$

y-intercept(s) in point form.

y-intercept(s): $(0, - 27)$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0), (\frac{1}{5}, 0)$

y-intercept(s): $(0, - 27)$

Step 4

Find the x and y Intercepts f(x)=(x+3)^3(5x-1)^3

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