Finite Math Examples

$2 r s + 3 r s t - 8 r - 12 r t$

Step 1

Factor out the GCF of $r$ from $2 r s + 3 r s t - 8 r - 12 r t$ .

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Step 1.1

Factor out the GCF of $r$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $r$ from the expression $2 r s$ .

$r (2 s) + 3 r s t - 8 r - 12 r t$

Step 1.1.2

Factor out the GCF of $r$ from the expression $3 r s t$ .

$r (2 s) + r (3 s t) - 8 r - 12 r t$

Step 1.1.3

Factor out the GCF of $r$ from the expression $- 8 r$ .

$r (2 s) + r (3 s t) + r (- 8) - 12 r t$

Step 1.1.4

Factor out the GCF of $r$ from the expression $- 12 r t$ .

$r (2 s) + r (3 s t) + r (- 8) + r (- 12 t)$

Step 1.2

Since all the terms share a common factor of $r$ , it can be factored out of each term.

$r (2 s + 3 s t - 8 - 12 t)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$r ((2 s + 3 s t) - 8 - 12 t)$

Step 2.2

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

$r (s \cdot (2 + 3 t) - 4 (2 + 3 t))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 + 3 t$ .

$r ((2 + 3 t) (s - 4))$