Precalculus Examples

$48 + 32 t - 16 t^{2}$

Step 1

Factor $- 16$ out of $48 + 32 t - 16 t^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $48$ .

$32 t - 16 t^{2} + 48$

Step 1.1.2

Reorder $32 t$ and $- 16 t^{2}$ .

$- 16 t^{2} + 32 t + 48$

Step 1.2

Factor $- 16$ out of $- 16 t^{2}$ .

$- 16 (t^{2}) + 32 t + 48$

Step 1.3

Factor $- 16$ out of $32 t$ .

$- 16 (t^{2}) - 16 (- 2 t) + 48$

Step 1.4

Factor $- 16$ out of $48$ .

$- 16 (t^{2}) - 16 (- 2 t) - 16 (- 3)$

Step 1.5

Factor $- 16$ out of $- 16 (t^{2}) - 16 (- 2 t)$ .

$- 16 (t^{2} - 2 t) - 16 (- 3)$

Step 1.6

Factor $- 16$ out of $- 16 (t^{2} - 2 t) - 16 (- 3)$ .

$- 16 (t^{2} - 2 t - 3)$

Step 2

Factor.

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Step 2.1

Factor $t^{2} - 2 t - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 2.1.2

Write the factored form using these integers.

$- 16 ((t - 3) (t + 1))$

Step 2.2

Remove unnecessary parentheses.

$- 16 (t - 3) (t + 1)$