Algebra Examples

$(- 4, \infty)$

Step 1

$x = - 4$ and $x = \infty$ are the two real distinct solutions for the quadratic equation, which means that $x + 4$ and $x + - \infty$ are the factors of the quadratic equation.

$(x + 4) (x + - \infty) = 0$

Step 2

Expand $(x + 4) (x + - \infty)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x + - \infty) + 4 (x + - \infty) = 0$

Step 2.2

Apply the distributive property.

$x \cdot x + x + - \infty + 4 (x + - \infty) = 0$

Step 2.3

Apply the distributive property.

$x \cdot x + x + - \infty + 4 x + 4 + - \infty = 0$

Step 3

Simplify each term.

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Step 3.1

Multiply $x$ by $x$ .

$x^{2} + x + - \infty + 4 x + 4 + - \infty = 0$

Step 3.2

A non-zero constant times infinity is infinity.

$x^{2} + x + - \infty + 4 x + - \infty = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 4, \infty}$ is $y = x^{2} + x + - \infty + 4 x + - \infty$ .

$y = x^{2} + x + - \infty + 4 x + - \infty$

Step 5