Find the x and y Intercepts f(x)=(5x^2-43x-70)/(x^2+8x)

$f (x) = \frac{5 x^{2} - 43 x - 70}{x^{2} + 8 x}$

Step 1

Find the x-intercepts.

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

$0 = \frac{5 x^{2} - 43 x - 70}{x^{2} + 8 x}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} - 43 x - 70 = 0$

Solve the equation for $x$ .

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 $a \cdot c = 5 \cdot - 70 = - 350$ and whose sum is $b = - 43$ .

Factor $- 43$ out of $- 43 x$ .

$5 x^{2} - 43 x - 70 = 0$

Rewrite $- 43$ as $7$ plus $- 50$

$5 x^{2} + (7 - 50) x - 70 = 0$

Apply the distributive property.

$5 x^{2} + 7 x - 50 x - 70 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 7 x) - 50 x - 70 = 0$

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

$x (5 x + 7) - 10 (5 x + 7) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 7$ .

$(5 x + 7) (x - 10) = 0$

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

$5 x + 7 = 0$

$x - 10 = 0$

Set $5 x + 7$ equal to $0$ and solve for $x$ .

Set $5 x + 7$ equal to $0$ .

$5 x + 7 = 0$

Solve $5 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$5 x = - 7$

Divide each term in $5 x = - 7$ by $5$ and simplify.

Divide each term in $5 x = - 7$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Set $x - 10$ equal to $0$ and solve for $x$ .

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

The final solution is all the values that make $(5 x + 7) (x - 10) = 0$ true.

$x = - \frac{7}{5}, 10$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{7}{5}, 0), (10, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2} - 43 \cdot 0 - 70}{{(0)}^{2} + 8 (0)}$

The equation has an undefined fraction.

Undefined

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(- \frac{7}{5}, 0), (10, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x)=(5x^2-43x-70)/(x^2+8x)

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