Find the x and y Intercepts f(x)=-15x^5-5x^4+10x^3

$f (x) = - 15 x^{5} - 5 x^{4} + 10 x^{3}$

Find the x-intercepts.

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

$0 = - 15 x^{5} - 5 x^{4} + 10 x^{3}$

Solve the equation.

Rewrite the equation as $- 15 x^{5} - 5 x^{4} + 10 x^{3} = 0$ .

$- 15 x^{5} - 5 x^{4} + 10 x^{3} = 0$

Factor the left side of the equation.

Factor $- 5 x^{3}$ out of $- 15 x^{5} - 5 x^{4} + 10 x^{3}$ .

Factor $- 5 x^{3}$ out of $- 15 x^{5}$ .

$- 5 x^{3} (3 x^{2}) - 5 x^{4} + 10 x^{3} = 0$

Factor $- 5 x^{3}$ out of $- 5 x^{4}$ .

$- 5 x^{3} (3 x^{2}) - 5 x^{3} x + 10 x^{3} = 0$

Factor $- 5 x^{3}$ out of $10 x^{3}$ .

$- 5 x^{3} (3 x^{2}) - 5 x^{3} x - 5 x^{3} \cdot - 2 = 0$

Factor $- 5 x^{3}$ out of $- 5 x^{3} (3 x^{2}) - 5 x^{3} (x)$ .

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

Factor $- 5 x^{3}$ out of $- 5 x^{3} (3 x^{2} + x) - 5 x^{3} (- 2)$ .

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

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

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

Rewrite $1$ as $- 2$ plus $3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

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

Remove unnecessary parentheses.

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

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

$x^{3} = 0$

$3 x - 2 = 0$

$x + 1 = 0$

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

Set $x^{3}$ equal to $0$ .

$x^{3} = 0$

Solve $x^{3} = 0$ for $x$ .

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

$x = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

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

$x = 0$

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

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

$3 x - 2 = 0$

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

Add $2$ to both sides of the equation.

$3 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$x = 0, \frac{2}{3}, - 1$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\frac{2}{3}, 0), (- 1, 0)$

Find the y-intercepts.

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

$y = - 15 {(0)}^{5} - 5 {(0)}^{4} + 10 {(0)}^{3}$

Solve the equation.

Remove parentheses.

$y = - 15 \cdot 0^{5} - 5 {(0)}^{4} + 10 {(0)}^{3}$

Remove parentheses.

$y = - 15 \cdot 0^{5} - 5 \cdot 0^{4} + 10 {(0)}^{3}$

Remove parentheses.

$y = - 15 \cdot 0^{5} - 5 \cdot 0^{4} + 10 \cdot 0^{3}$

Remove parentheses.

$y = - 15 {(0)}^{5} - 5 {(0)}^{4} + 10 {(0)}^{3}$

Simplify $- 15 {(0)}^{5} - 5 {(0)}^{4} + 10 {(0)}^{3}$ .

Simplify each term.

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

$y = - 15 \cdot 0 - 5 {(0)}^{4} + 10 {(0)}^{3}$

Multiply $- 15$ by $0$ .

$y = 0 - 5 {(0)}^{4} + 10 {(0)}^{3}$

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

$y = 0 - 5 \cdot 0 + 10 {(0)}^{3}$

Multiply $- 5$ by $0$ .

$y = 0 + 0 + 10 {(0)}^{3}$

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

$y = 0 + 0 + 10 \cdot 0$

Multiply $10$ by $0$ .

$y = 0 + 0 + 0$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (\frac{2}{3}, 0), (- 1, 0)$

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

Find the x and y Intercepts f(x)=-15x^5-5x^4+10x^3

Related Questions

Support LCMGCF.com by disabling your adblocker.