Trigonometry Examples

$45 x^{2} + 78 x + 24$

Step 1

Factor $3$ out of $45 x^{2} + 78 x + 24$ .

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Step 1.1

Factor $3$ out of $45 x^{2}$ .

$3 (15 x^{2}) + 78 x + 24$

Step 1.2

Factor $3$ out of $78 x$ .

$3 (15 x^{2}) + 3 (26 x) + 24$

Step 1.3

Factor $3$ out of $24$ .

$3 (15 x^{2}) + 3 (26 x) + 3 (8)$

Step 1.4

Factor $3$ out of $3 (15 x^{2}) + 3 (26 x)$ .

$3 (15 x^{2} + 26 x) + 3 (8)$

Step 1.5

Factor $3$ out of $3 (15 x^{2} + 26 x) + 3 (8)$ .

$3 (15 x^{2} + 26 x + 8)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 15 \cdot 8 = 120$ and whose sum is $b = 26$ .

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Step 2.1.1.1

Factor $26$ out of $26 x$ .

$3 (15 x^{2} + 26 (x) + 8)$

Step 2.1.1.2

Rewrite $26$ as $6$ plus $20$

$3 (15 x^{2} + (6 + 20) x + 8)$

Step 2.1.1.3

Apply the distributive property.

$3 (15 x^{2} + 6 x + 20 x + 8)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$3 ((15 x^{2} + 6 x) + 20 x + 8)$

Step 2.1.2.2

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

$3 (3 x (5 x + 2) + 4 (5 x + 2))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$3 ((5 x + 2) (3 x + 4))$

Step 2.2

Remove unnecessary parentheses.

$3 (5 x + 2) (3 x + 4)$