Basic Math Examples

$10 - 19 a + 6 a^{2}$

Step 1

Reorder terms.

$6 a^{2} - 19 a + 10$

Step 2

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 $a \cdot c = 6 \cdot 10 = 60$ and whose sum is $b = - 19$ .

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Step 2.1

Factor $- 19$ out of $- 19 a$ .

$6 a^{2} - 19 (a) + 10$

Step 2.2

Rewrite $- 19$ as $- 4$ plus $- 15$

$6 a^{2} + (- 4 - 15) a + 10$

Step 2.3

Apply the distributive property.

$6 a^{2} - 4 a - 15 a + 10$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$(6 a^{2} - 4 a) - 15 a + 10$

Step 3.2

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

$2 a (3 a - 2) - 5 (3 a - 2)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $3 a - 2$ .

$(3 a - 2) (2 a - 5)$