Basic Math Examples

4 w^{2} - 52 w - 120

$4 w^{2} - 52 w - 120$

Step 1

Factor

$4$ out of

$4 w^{2} - 52 w - 120$ .

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Step 1.1

Factor

$4$ out of

$4 w^{2}$ .

$4 (w^{2}) - 52 w - 120$

Step 1.2

Factor

$4$ out of

$- 52 w$ .

$4 (w^{2}) + 4 (- 13 w) - 120$

Step 1.3

Factor

$4$ out of

$- 120$ .

$4 w^{2} + 4 (- 13 w) + 4 \cdot - 30$

Step 1.4

Factor

$4$ out of

$4 w^{2} + 4 (- 13 w)$ .

$4 (w^{2} - 13 w) + 4 \cdot - 30$

Step 1.5

Factor

$4$ out of

$4 (w^{2} - 13 w) + 4 \cdot - 30$ .

$4 (w^{2} - 13 w - 30)$

$4 (w^{2} - 13 w - 30)$

Step 2

Factor.

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Step 2.1

Factor

$w^{2} - 13 w - 30$ using the AC method.

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Step 2.1.1

Consider the form

$x^{2} + b x + c$ . Find a pair of integers whose product is

$c$ and whose sum is

$b$ . In this case, whose product is

$- 30$ and whose sum is

$- 13$ .

$- 15, 2$

Step 2.1.2

Write the factored form using these integers.

$4 ((w - 15) (w + 2))$

$4 ((w - 15) (w + 2))$

Step 2.2

Remove unnecessary parentheses.

$4 (w - 15) (w + 2)$

$4 (w - 15) (w + 2)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$