Finite Math Examples

$6 s^{2} - 5 s t + 1 t^{2}$

Step 1

Factor by grouping.

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Step 1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot 1 = 6$ and whose sum is $b = - 5$ .

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Step 1.1.1

Reorder terms.

$6 s^{2} + 1 t^{2} - 5 s t$

Step 1.1.2

Reorder $1 t^{2}$ and $- 5 s t$ .

$6 s^{2} - 5 s t + 1 t^{2}$

Step 1.1.3

Factor $- 5$ out of $- 5 s t$ .

$6 s^{2} - 5 (s t) + 1 t^{2}$

Step 1.1.4

Rewrite $- 5$ as $- 2$ plus $- 3$

$6 s^{2} + (- 2 - 3) (s t) + 1 t^{2}$

Step 1.1.5

Apply the distributive property.

$6 s^{2} - 2 (s t) - 3 (s t) + 1 t^{2}$

Step 1.1.6

Remove unnecessary parentheses.

$6 s^{2} - 2 s t - 3 (s t) + 1 t^{2}$

Step 1.1.7

Remove unnecessary parentheses.

$6 s^{2} - 2 s t - 3 s t + 1 t^{2}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$(6 s^{2} - 2 s t) - 3 s t + 1 t^{2}$

Step 1.2.2

Factor out the greatest common factor (GCF) from each group.

$2 s (3 s - 1 t) - t (3 s - t)$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $3 s - 1 t$ .

$(3 s - 1 t) (2 s - t)$

Step 2

Rewrite $- 1 t$ as $- t$ .

$(3 s - t) (2 s - t)$