Find the x and y Intercepts f(x)=(x-5)(x-3)(4x+8)

$f (x) = (x - 5) (x - 3) (4 x + 8)$

Step 1

Find the x-intercepts.

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

$0 = (x - 5) (x - 3) (4 x + 8)$

Solve the equation.

Rewrite the equation as $(x - 5) (x - 3) (4 x + 8) = 0$ .

$(x - 5) (x - 3) (4 x + 8) = 0$

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

$x - 5 = 0$

$x - 3 = 0$

$4 x + 8 = 0$

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

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $4 x + 8$ equal to $0$ and solve for $x$ .

Set $4 x + 8$ equal to $0$ .

$4 x + 8 = 0$

Solve $4 x + 8 = 0$ for $x$ .

Subtract $8$ from both sides of the equation.

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

The final solution is all the values that make $(x - 5) (x - 3) (4 x + 8) = 0$ true.

$x = 5, 3, - 2$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (3, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$y = ((0) - 5) ((0) - 3) (4 (0) + 8)$

Solve the equation.

Remove parentheses.

$y = (0 - 5) ((0) - 3) (4 (0) + 8)$

Remove parentheses.

$y = (0 - 5) (0 - 3) (4 (0) + 8)$

Remove parentheses.

$y = ((0) - 5) ((0) - 3) (4 (0) + 8)$

Simplify $((0) - 5) ((0) - 3) (4 (0) + 8)$ .

Subtract $5$ from $0$ .

$y = - 5 ((0) - 3) (4 (0) + 8)$

Subtract $3$ from $0$ .

$y = - 5 \cdot - 3 (4 (0) + 8)$

Multiply $- 5$ by $- 3$ .

$y = 15 (4 (0) + 8)$

Multiply $4$ by $0$ .

$y = 15 (0 + 8)$

Add $0$ and $8$ .

$y = 15 \cdot 8$

Multiply $15$ by $8$ .

$y = 120$

y-intercept(s) in point form.

y-intercept(s): $(0, 120)$

Step 3

List the intersections.

x-intercept(s): $(5, 0), (3, 0), (- 2, 0)$

y-intercept(s): $(0, 120)$

Step 4

Find the x and y Intercepts f(x)=(x-5)(x-3)(4x+8)

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