Find the x and y Intercepts f(x)=4(x+4)(2x+5)^2(x+4)

$f (x) = 4 (x + 4) {(2 x + 5)}^{2} (x + 4)$

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $4 (x + 4) {(2 x + 5)}^{2} (x + 4) = 0$ .

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

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

$x + 4 = 0$

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

$x + 4 = 0$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

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

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

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

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

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

$2 x + 5 = 0$

Solve for $x$ .

Subtract $5$ from both sides of the equation.

$2 x = - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $4 (x + 4) {(2 x + 5)}^{2} (x + 4) = 0$ true.

$x = - 4, - \frac{5}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (- \frac{5}{2}, 0)$

Find the y-intercepts.

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

$y = 4 ((0) + 4) {(2 (0) + 5)}^{2} ((0) + 4)$

Solve the equation.

Remove parentheses.

$y = 4 (0 + 4) {(2 (0) + 5)}^{2} ((0) + 4)$

Remove parentheses.

$y = 4 (0 + 4) {(2 (0) + 5)}^{2} (0 + 4)$

Remove parentheses.

$y = 4 ((0) + 4) {(2 (0) + 5)}^{2} ((0) + 4)$

Simplify $4 ((0) + 4) {(2 (0) + 5)}^{2} ((0) + 4)$ .

Add $0$ and $4$ .

$y = 4 \cdot 4 {(2 (0) + 5)}^{2} ((0) + 4)$

Multiply $4$ by $4$ .

$y = 16 {(2 (0) + 5)}^{2} ((0) + 4)$

Multiply $2$ by $0$ .

$y = 16 {(0 + 5)}^{2} ((0) + 4)$

Add $0$ and $5$ .

$y = 16 \cdot 5^{2} ((0) + 4)$

Raise $5$ to the power of $2$ .

$y = 16 \cdot 25 ((0) + 4)$

Multiply $16$ by $25$ .

$y = 400 ((0) + 4)$

Add $0$ and $4$ .

$y = 400 \cdot 4$

Multiply $400$ by $4$ .

$y = 1600$

y-intercept(s) in point form.

y-intercept(s): $(0, 1600)$

List the intersections.

x-intercept(s): $(- 4, 0), (- \frac{5}{2}, 0)$

y-intercept(s): $(0, 1600)$

Find the x and y Intercepts f(x)=4(x+4)(2x+5)^2(x+4)

Related Questions

Support LCMGCF.com by disabling your adblocker.