Find the x and y Intercepts (x+4)^6(x+7)^5

${(x + 4)}^{6} {(x + 7)}^{5}$

Step 1

Write ${(x + 4)}^{6} {(x + 7)}^{5}$ as an equation.

$y = {(x + 4)}^{6} {(x + 7)}^{5}$

Step 2

Find the x-intercepts.

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

$0 = {(x + 4)}^{6} {(x + 7)}^{5}$

Solve the equation.

Rewrite the equation as ${(x + 4)}^{6} {(x + 7)}^{5} = 0$ .

${(x + 4)}^{6} {(x + 7)}^{5} = 0$

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

${(x + 4)}^{6} = 0$

${(x + 7)}^{5} = 0$

Set ${(x + 4)}^{6}$ equal to $0$ and solve for $x$ .

Set ${(x + 4)}^{6}$ equal to $0$ .

${(x + 4)}^{6} = 0$

Solve ${(x + 4)}^{6} = 0$ for $x$ .

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set ${(x + 7)}^{5}$ equal to $0$ and solve for $x$ .

Set ${(x + 7)}^{5}$ equal to $0$ .

${(x + 7)}^{5} = 0$

Solve ${(x + 7)}^{5} = 0$ for $x$ .

Set the $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make ${(x + 4)}^{6} {(x + 7)}^{5} = 0$ true.

$x = - 4, - 7$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (- 7, 0)$

Step 3

Find the y-intercepts.

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

$y = {((0) + 4)}^{6} {((0) + 7)}^{5}$

Solve the equation.

Remove parentheses.

$y = {(0 + 4)}^{6} {((0) + 7)}^{5}$

Remove parentheses.

$y = {(0 + 4)}^{6} {(0 + 7)}^{5}$

Remove parentheses.

$y = {((0) + 4)}^{6} {((0) + 7)}^{5}$

Simplify ${((0) + 4)}^{6} {((0) + 7)}^{5}$ .

Add $0$ and $4$ .

$y = 4^{6} {((0) + 7)}^{5}$

Raise $4$ to the power of $6$ .

$y = 4096 {((0) + 7)}^{5}$

Add $0$ and $7$ .

$y = 4096 \cdot 7^{5}$

Raise $7$ to the power of $5$ .

$y = 4096 \cdot 16807$

Multiply $4096$ by $16807$ .

$y = 68841472$

y-intercept(s) in point form.

y-intercept(s): $(0, 68841472)$

Step 4

List the intersections.

x-intercept(s): $(- 4, 0), (- 7, 0)$

y-intercept(s): $(0, 68841472)$

Step 5

Find the x and y Intercepts (x+4)^6(x+7)^5

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