Precalculus Examples

$3 x^{2} - 38 x - 13$

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 $a \cdot c = 3 \cdot - 13 = - 39$ and whose sum is $b = - 38$ .

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Step 1.1

Factor $- 38$ out of $- 38 x$ .

$3 x^{2} - 38 (x) - 13$

Step 1.2

Rewrite $- 38$ as $1$ plus $- 39$

$3 x^{2} + (1 - 39) x - 13$

Step 1.3

Apply the distributive property.

$3 x^{2} + 1 x - 39 x - 13$

Step 1.4

Multiply $x$ by $1$ .

$3 x^{2} + x - 39 x - 13$

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.

$(3 x^{2} + x) - 39 x - 13$

Step 2.2

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

$x (3 x + 1) - 13 (3 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$(3 x + 1) (x - 13)$