Trigonometry Examples

$14 z^{2} + z - 3$

Step 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 $a \cdot c = 14 \cdot - 3 = - 42$ and whose sum is $b = 1$ .

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Step 1.1

Multiply by $1$ .

$14 z^{2} + 1 z - 3$

Step 1.2

Rewrite $1$ as $- 6$ plus $7$

$14 z^{2} + (- 6 + 7) z - 3$

Step 1.3

Apply the distributive property.

$14 z^{2} - 6 z + 7 z - 3$

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.

$(14 z^{2} - 6 z) + 7 z - 3$

Step 2.2

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

$2 z (7 z - 3) + 1 (7 z - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 z - 3$ .

$(7 z - 3) (2 z + 1)$