Find the x and y Intercepts f(x)=(x-7)(5x+1)^2(x-7)

$f (x) = (x - 7) {(5 x + 1)}^{2} (x - 7)$

Step 1

Find the x-intercepts.

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

$0 = (x - 7) {(5 x + 1)}^{2} (x - 7)$

Solve the equation.

Rewrite the equation as $(x - 7) {(5 x + 1)}^{2} (x - 7) = 0$ .

$(x - 7) {(5 x + 1)}^{2} (x - 7) = 0$

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

$x - 7 = 0$

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

$x - 7 = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Set ${(5 x + 1)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(5 x + 1)}^{2}$ equal to $0$ .

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

Solve ${(5 x + 1)}^{2} = 0$ for $x$ .

Set the $5 x + 1$ equal to $0$ .

$5 x + 1 = 0$

Solve for $x$ .

Subtract $1$ from both sides of the equation.

$5 x = - 1$

Divide each term in $5 x = - 1$ by $5$ and simplify.

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

The final solution is all the values that make $(x - 7) {(5 x + 1)}^{2} (x - 7) = 0$ true.

$x = 7, - \frac{1}{5}$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- \frac{1}{5}, 0)$

Step 2

Find the y-intercepts.

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

$y = ((0) - 7) {(5 (0) + 1)}^{2} ((0) - 7)$

Solve the equation.

Remove parentheses.

$y = (0 - 7) {(5 (0) + 1)}^{2} ((0) - 7)$

Remove parentheses.

$y = (0 - 7) {(5 (0) + 1)}^{2} (0 - 7)$

Remove parentheses.

$y = ((0) - 7) {(5 (0) + 1)}^{2} ((0) - 7)$

Simplify $((0) - 7) {(5 (0) + 1)}^{2} ((0) - 7)$ .

Subtract $7$ from $0$ .

$y = - 7 {(5 (0) + 1)}^{2} ((0) - 7)$

Multiply $5$ by $0$ .

$y = - 7 {(0 + 1)}^{2} ((0) - 7)$

Add $0$ and $1$ .

$y = - 7 \cdot 1^{2} ((0) - 7)$

One to any power is one.

$y = - 7 \cdot 1 ((0) - 7)$

Multiply $- 7$ by $1$ .

$y = - 7 ((0) - 7)$

Subtract $7$ from $0$ .

$y = - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$y = 49$

y-intercept(s) in point form.

y-intercept(s): $(0, 49)$

Step 3

List the intersections.

x-intercept(s): $(7, 0), (- \frac{1}{5}, 0)$

y-intercept(s): $(0, 49)$

Step 4

Find the x and y Intercepts f(x)=(x-7)(5x+1)^2(x-7)

Related Questions

Support LCMGCF.com by disabling your adblocker.