Algebra Examples

3 a^{2} - 4 a - 20

$3 a^{2} - 4 a - 20$

Step 1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 3 \cdot - 20 = - 60

$a \cdot c = 3 \cdot - 20 = - 60$ and whose sum is

b = - 4

$b = - 4$ .

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Step 1.1

Factor

- 4

$- 4$ out of

- 4 a

$- 4 a$ .

3 a^{2} - 4 (a) - 20

$3 a^{2} - 4 (a) - 20$

Step 1.2

Rewrite

- 4

$- 4$ as

6

$6$ plus

- 10

$- 10$

3 a^{2} + (6 - 10) a - 20

$3 a^{2} + (6 - 10) a - 20$

Step 1.3

Apply the distributive property.

3 a^{2} + 6 a - 10 a - 20

$3 a^{2} + 6 a - 10 a - 20$

3 a^{2} + 6 a - 10 a - 20

$3 a^{2} + 6 a - 10 a - 20$

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 a^{2} + 6 a) - 10 a - 20

$(3 a^{2} + 6 a) - 10 a - 20$

Step 2.2

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

3 a (a + 2) - 10 (a + 2)

$3 a (a + 2) - 10 (a + 2)$

3 a (a + 2) - 10 (a + 2)

$3 a (a + 2) - 10 (a + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

a + 2

$a + 2$ .

(a + 2) (3 a - 10)

$(a + 2) (3 a - 10)$