Algebra Examples

3 x^{2} + 10 x - 8

$3 x^{2} + 10 x - 8$

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 - 8 = - 24

$a \cdot c = 3 \cdot - 8 = - 24$ and whose sum is

b = 10

$b = 10$ .

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Step 1.1

Factor

10

$10$ out of

10 x

$10 x$ .

3 x^{2} + 10 (x) - 8

$3 x^{2} + 10 (x) - 8$

Step 1.2

Rewrite

10

$10$ as

- 2

$- 2$ plus

12

$12$

3 x^{2} + (- 2 + 12) x - 8

$3 x^{2} + (- 2 + 12) x - 8$

Step 1.3

Apply the distributive property.

3 x^{2} - 2 x + 12 x - 8

$3 x^{2} - 2 x + 12 x - 8$

3 x^{2} - 2 x + 12 x - 8

$3 x^{2} - 2 x + 12 x - 8$

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} - 2 x) + 12 x - 8

$(3 x^{2} - 2 x) + 12 x - 8$

Step 2.2

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

x (3 x - 2) + 4 (3 x - 2)

$x (3 x - 2) + 4 (3 x - 2)$

x (3 x - 2) + 4 (3 x - 2)

$x (3 x - 2) + 4 (3 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 x - 2

$3 x - 2$ .

(3 x - 2) (x + 4)

$(3 x - 2) (x + 4)$