Pre-Algebra Examples

$(16 x^{2} + 6 x^{3} - 18 x - 48) \div (3 x + 8)$

Step 1

Rewrite the division as a fraction.

$\frac{16 x^{2} + 6 x^{3} - 18 x - 48}{3 x + 8}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Factor $2$ out of $16 x^{2} + 6 x^{3} - 18 x - 48$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $16 x^{2}$ .

$\frac{2 (8 x^{2}) + 6 x^{3} - 18 x - 48}{3 x + 8}$

Step 2.1.2

Factor $2$ out of $6 x^{3}$ .

$\frac{2 (8 x^{2}) + 2 (3 x^{3}) - 18 x - 48}{3 x + 8}$

Step 2.1.3

Factor $2$ out of $- 18 x$ .

$\frac{2 (8 x^{2}) + 2 (3 x^{3}) + 2 (- 9 x) - 48}{3 x + 8}$

Step 2.1.4

Factor $2$ out of $- 48$ .

$\frac{2 (8 x^{2}) + 2 (3 x^{3}) + 2 (- 9 x) + 2 (- 24)}{3 x + 8}$

Step 2.1.5

Factor $2$ out of $2 (8 x^{2}) + 2 (3 x^{3})$ .

$\frac{2 (8 x^{2} + 3 x^{3}) + 2 (- 9 x) + 2 (- 24)}{3 x + 8}$

Step 2.1.6

Factor $2$ out of $2 (8 x^{2} + 3 x^{3}) + 2 (- 9 x)$ .

$\frac{2 (8 x^{2} + 3 x^{3} - 9 x) + 2 (- 24)}{3 x + 8}$

Step 2.1.7

Factor $2$ out of $2 (8 x^{2} + 3 x^{3} - 9 x) + 2 (- 24)$ .

$\frac{2 (8 x^{2} + 3 x^{3} - 9 x - 24)}{3 x + 8}$

Step 2.2

Reorder terms.

$\frac{2 (3 x^{3} + 8 x^{2} - 9 x - 24)}{3 x + 8}$

Step 2.3

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.3.1

Group the first two terms and the last two terms.

$\frac{2 ((3 x^{3} + 8 x^{2}) - 9 x - 24)}{3 x + 8}$

Step 2.3.2

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

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

Step 2.4

Factor the polynomial by factoring out the greatest common factor, $3 x + 8$ .

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

Step 3

Cancel the common factor of $3 x + 8$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $2 (x^{2} - 3)$ by $1$ .

$2 (x^{2} - 3)$

Step 4

Apply the distributive property.

$2 x^{2} + 2 \cdot - 3$

Step 5

Multiply $2$ by $- 3$ .

$2 x^{2} - 6$