Finite Math Examples

$z^{2} + (3 + 2 i) z + 6 i$

Step 1

Apply the distributive property.

$z^{2} + 3 z + 2 i z + 6 i$

Step 2

Reorder terms.

$z^{2} + 2 i z + 3 z + 6 i$

Step 3

Rewrite $z^{2} + 2 i z + 3 z + 6 i$ in a factored form.

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Step 3.1

Factor out the greatest common factor from each group.

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Step 3.1.1

Group the first two terms and the last two terms.

$(z^{2} + 2 i z) + 3 z + 6 i$

Step 3.1.2

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

$z (z + 2 i) + 3 (z + 2 i)$

Step 3.2

Factor the polynomial by factoring out the greatest common factor, $z + 2 i$ .

$(z + 2 i) (z + 3)$