Pre-Algebra Examples

$\frac{t^{2} - 6 t - 16}{t^{2} - 8 t + 15}$

Step 1

Factor $t^{2} - 6 t - 16$ using the AC method.

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Step 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 $- 16$ and whose sum is $- 6$ .

$- 8, 2$

Step 1.2

Write the factored form using these integers.

$\frac{(t - 8) (t + 2)}{t^{2} - 8 t + 15}$

Step 2

Factor $t^{2} - 8 t + 15$ using the AC method.

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Step 2.1

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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Step 2.2

Write the factored form using these integers.

$\frac{(t - 8) (t + 2)}{(t - 5) (t - 3)}$