Algebra Examples

$(- \infty, - 2)$

Step 1

$x = - \infty$ and $x = - 2$ are the two real distinct solutions for the quadratic equation, which means that $x + \infty$ and $x + 2$ are the factors of the quadratic equation.

$(x + \infty) (x + 2) = 0$

Step 2

Expand $(x + \infty) (x + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x + 2) + \infty (x + 2) = 0$

Step 2.2

Apply the distributive property.

$x \cdot x + x \cdot 2 + \infty (x + 2) = 0$

Step 2.3

Apply the distributive property.

$x \cdot x + x \cdot 2 + \infty x + \infty \cdot 2 = 0$

Step 3

Simplify each term.

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Step 3.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 + \infty x + \infty \cdot 2 = 0$

Step 3.2

Move $2$ to the left of $x$ .

$x^{2} + 2 \cdot x + \infty x + \infty \cdot 2 = 0$

Step 3.3

A non-zero constant times infinity is infinity.

$x^{2} + 2 x + \infty x + \infty = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- \infty, - 2}$ is $y = x^{2} + 2 x + \infty x + \infty$ .

$y = x^{2} + 2 x + \infty x + \infty$

Step 5