Precalculus Examples

$27 x^{2} - 15 x + 2$

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 $a \cdot c = 27 \cdot 2 = 54$ and whose sum is $b = - 15$ .

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Step 1.1

Factor $- 15$ out of $- 15 x$ .

$27 x^{2} - 15 (x) + 2$

Step 1.2

Rewrite $- 15$ as $- 6$ plus $- 9$

$27 x^{2} + (- 6 - 9) x + 2$

Step 1.3

Apply the distributive property.

$27 x^{2} - 6 x - 9 x + 2$

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.

$(27 x^{2} - 6 x) - 9 x + 2$

Step 2.2

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

$3 x (9 x - 2) - (9 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $9 x - 2$ .

$(9 x - 2) (3 x - 1)$