Pre-Algebra Examples

$6 x^{2} + x - 40$

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 $a \cdot c = 6 \cdot - 40 = - 240$ and whose sum is $b = 1$ .

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Step 1.1

Multiply by $1$ .

$6 x^{2} + 1 x - 40$

Step 1.2

Rewrite $1$ as $- 15$ plus $16$

$6 x^{2} + (- 15 + 16) x - 40$

Step 1.3

Apply the distributive property.

$6 x^{2} - 15 x + 16 x - 40$

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.

$(6 x^{2} - 15 x) + 16 x - 40$

Step 2.2

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

$3 x (2 x - 5) + 8 (2 x - 5)$

Step 3

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

$(2 x - 5) (3 x + 8)$