Trigonometry Examples

$6 x^{2} + 19 x + 3$

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 $a \cdot c = 6 \cdot 3 = 18$ and whose sum is $b = 19$ .

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Step 1.1

Factor $19$ out of $19 x$ .

$6 x^{2} + 19 (x) + 3$

Step 1.2

Rewrite $19$ as $1$ plus $18$

$6 x^{2} + (1 + 18) x + 3$

Step 1.3

Apply the distributive property.

$6 x^{2} + 1 x + 18 x + 3$

Step 1.4

Multiply $x$ by $1$ .

$6 x^{2} + x + 18 x + 3$

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.

$(6 x^{2} + x) + 18 x + 3$

Step 2.2

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

$x (6 x + 1) + 3 (6 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x + 1$ .

$(6 x + 1) (x + 3)$