Find the x and y Intercepts y=x^2(x^2-7)(2x+3)

$y = x^{2} (x^{2} - 7) (2 x + 3)$

Find the x-intercepts.

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

$0 = x^{2} (x^{2} - 7) (2 x + 3)$

Solve the equation.

Rewrite the equation as $x^{2} (x^{2} - 7) (2 x + 3) = 0$ .

$x^{2} (x^{2} - 7) (2 x + 3) = 0$

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

$x^{2} = 0$

$x^{2} - 7 = 0$

$2 x + 3 = 0$

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $x^{2} - 7$ equal to $0$ and solve for $x$ .

Set $x^{2} - 7$ equal to $0$ .

$x^{2} - 7 = 0$

Solve $x^{2} - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$x^{2} = 7$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{7}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{7}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{7}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{7}, - \sqrt{7}$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

The final solution is all the values that make $x^{2} (x^{2} - 7) (2 x + 3) = 0$ true.

$x = 0, \sqrt{7}, - \sqrt{7}, - \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\sqrt{7}, 0), (- \sqrt{7}, 0), (- \frac{3}{2}, 0)$

Find the y-intercepts.

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

$y = {(0)}^{2} ({(0)}^{2} - 7) (2 (0) + 3)$

Solve the equation.

Remove parentheses.

$y = 0^{2} ({(0)}^{2} - 7) (2 (0) + 3)$

Remove parentheses.

$y = 0^{2} (0^{2} - 7) (2 (0) + 3)$

Remove parentheses.

$y = {(0)}^{2} ({(0)}^{2} - 7) (2 (0) + 3)$

Simplify ${(0)}^{2} ({(0)}^{2} - 7) (2 (0) + 3)$ .

Raising $0$ to any positive power yields $0$ .

$y = 0 ({(0)}^{2} - 7) (2 (0) + 3)$

Raising $0$ to any positive power yields $0$ .

$y = 0 (0 - 7) (2 (0) + 3)$

Subtract $7$ from $0$ .

$y = 0 \cdot - 7 (2 (0) + 3)$

Multiply $0$ by $- 7$ .

$y = 0 (2 (0) + 3)$

Multiply $2$ by $0$ .

$y = 0 (0 + 3)$

Add $0$ and $3$ .

$y = 0 \cdot 3$

Multiply $0$ by $3$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (\sqrt{7}, 0), (- \sqrt{7}, 0), (- \frac{3}{2}, 0)$

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

Find the x and y Intercepts y=x^2(x^2-7)(2x+3)

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