Algebra Examples

3 x^{2} + 8 x - 16

$3 x^{2} + 8 x - 16$

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 - 16 = - 48

$a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is

b = 8

$b = 8$ .

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Step 1.1

Factor

8

$8$ out of

8 x

$8 x$ .

3 x^{2} + 8 (x) - 16

$3 x^{2} + 8 (x) - 16$

Step 1.2

Rewrite

8

$8$ as

- 4

$- 4$ plus

12

$12$

3 x^{2} + (- 4 + 12) x - 16

$3 x^{2} + (- 4 + 12) x - 16$

Step 1.3

Apply the distributive property.

3 x^{2} - 4 x + 12 x - 16

$3 x^{2} - 4 x + 12 x - 16$

3 x^{2} - 4 x + 12 x - 16

$3 x^{2} - 4 x + 12 x - 16$

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} - 4 x) + 12 x - 16

$(3 x^{2} - 4 x) + 12 x - 16$

Step 2.2

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

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

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 x - 4

$3 x - 4$ .

(3 x - 4) (x + 4)

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