Algebra Examples

$f (x) = (x + 6) (x + 6) (x^{2} - 6)$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = (x + 6) (x + 6) (x^{2} - 6)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $(x + 6) (x + 6) (x^{2} - 6) = 0$ .

$(x + 6) (x + 6) (x^{2} - 6) = 0$

Step 1.2.2

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

$x + 6 = 0$

$x^{2} - 6 = 0$

Step 1.2.3

Set $x + 6$ equal to $0$ and solve for $x$ .

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Step 1.2.3.1

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Step 1.2.3.2

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 1.2.4

Set $x^{2} - 6$ equal to $0$ and solve for $x$ .

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Step 1.2.4.1

Set $x^{2} - 6$ equal to $0$ .

$x^{2} - 6 = 0$

Step 1.2.4.2

Solve $x^{2} - 6 = 0$ for $x$ .

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Step 1.2.4.2.1

Add $6$ to both sides of the equation.

$x^{2} = 6$

Step 1.2.4.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{6}$

Step 1.2.4.2.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.2.4.2.3.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{6}$

Step 1.2.4.2.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{6}$

Step 1.2.4.2.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{6}, - \sqrt{6}$

Step 1.2.5

The final solution is all the values that make $(x + 6) (x + 6) (x^{2} - 6) = 0$ true.

$x = - 6, \sqrt{6}, - \sqrt{6}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = ((0) + 6) ((0) + 6) ({(0)}^{2} - 6)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = (0 + 6) ((0) + 6) ({(0)}^{2} - 6)$

Step 2.2.2

Remove parentheses.

$y = (0 + 6) (0 + 6) ({(0)}^{2} - 6)$

Step 2.2.3

Remove parentheses.

$y = (0 + 6) (0 + 6) (0^{2} - 6)$

Step 2.2.4

Remove parentheses.

$y = ((0) + 6) ((0) + 6) ({(0)}^{2} - 6)$

Step 2.2.5

Simplify $((0) + 6) ((0) + 6) ({(0)}^{2} - 6)$ .

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Step 2.2.5.1

Add $0$ and $6$ .

$y = 6 ((0) + 6) ({(0)}^{2} - 6)$

Step 2.2.5.2

Add $0$ and $6$ .

$y = 6 \cdot 6 ({(0)}^{2} - 6)$

Step 2.2.5.3

Multiply $6$ by $6$ .

$y = 36 ({(0)}^{2} - 6)$

Step 2.2.5.4

Raising $0$ to any positive power yields $0$ .

$y = 36 (0 - 6)$

Step 2.2.5.5

Subtract $6$ from $0$ .

$y = 36 \cdot - 6$

Step 2.2.5.6

Multiply $36$ by $- 6$ .

$y = - 216$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 216)$

Step 3

List the intersections.

x-intercept(s): $(- 6, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

y-intercept(s): $(0, - 216)$

Step 4