Finite Math Examples

$3 + 16 u^{2} + 14 u$

Step 1

Reorder terms.

$16 u^{2} + 14 u + 3$

Step 2

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 $a \cdot c = 16 \cdot 3 = 48$ and whose sum is $b = 14$ .

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Step 2.1

Factor $14$ out of $14 u$ .

$16 u^{2} + 14 (u) + 3$

Step 2.2

Rewrite $14$ as $6$ plus $8$

$16 u^{2} + (6 + 8) u + 3$

Step 2.3

Apply the distributive property.

$16 u^{2} + 6 u + 8 u + 3$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$(16 u^{2} + 6 u) + 8 u + 3$

Step 3.2

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

$2 u (8 u + 3) + 1 (8 u + 3)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $8 u + 3$ .

$(8 u + 3) (2 u + 1)$