Find the x and y Intercepts f(x)=x(x+6)(x^2+1)(5x-3)

$f (x) = x (x + 6) (x^{2} + 1) (5 x - 3)$

Find the x-intercepts.

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

$0 = x (x + 6) (x^{2} + 1) (5 x - 3)$

Solve the equation.

Rewrite the equation as $x (x + 6) (x^{2} + 1) (5 x - 3) = 0$ .

$x (x + 6) (x^{2} + 1) (5 x - 3) = 0$

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

$x = 0$

$x + 6 = 0$

$x^{2} + 1 = 0$

$5 x - 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Set $x^{2} + 1$ equal to $0$ and solve for $x$ .

Set $x^{2} + 1$ equal to $0$ .

$x^{2} + 1 = 0$

Solve $x^{2} + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$x^{2} = - 1$

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

$x = \pm \sqrt{- 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

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.

$x = i$

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

$x = - i$

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

$x = i, - i$

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

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

$5 x - 3 = 0$

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

Add $3$ to both sides of the equation.

$5 x = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

The final solution is all the values that make $x (x + 6) (x^{2} + 1) (5 x - 3) = 0$ true.

$x = 0, - 6, i, - i, \frac{3}{5}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 6, 0), (\frac{3}{5}, 0)$

Find the y-intercepts.

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

$y = (0) ((0) + 6) ({(0)}^{2} + 1) (5 (0) - 3)$

Solve the equation.

Remove parentheses.

$y = 0 (0 + 6) ({(0)}^{2} + 1) (5 (0) - 3)$

Remove parentheses.

$y = 0 (0 + 6) (0^{2} + 1) (5 (0) - 3)$

Remove parentheses.

$y = (0) ((0) + 6) ({(0)}^{2} + 1) (5 (0) - 3)$

Simplify $(0) ((0) + 6) ({(0)}^{2} + 1) (5 (0) - 3)$ .

Add $0$ and $6$ .

$y = 0 \cdot 6 ({(0)}^{2} + 1) (5 (0) - 3)$

Multiply $0$ by $6$ .

$y = 0 ({(0)}^{2} + 1) (5 (0) - 3)$

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

$y = 0 (0 + 1) (5 (0) - 3)$

Add $0$ and $1$ .

$y = 0 \cdot 1 (5 (0) - 3)$

Multiply $0$ by $1$ .

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

Multiply $5$ by $0$ .

$y = 0 (0 - 3)$

Subtract $3$ from $0$ .

$y = 0 \cdot - 3$

Multiply $0$ by $- 3$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (- 6, 0), (\frac{3}{5}, 0)$

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

Find the x and y Intercepts f(x)=x(x+6)(x^2+1)(5x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.