Divide (2x^3-x^2-24x+12)÷(2x-1)

$(2 x^{3} - x^{2} - 24 x + 12) \div (2 x - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{2 x^{3} - x^{2} - 24 x + 12}{2 x - 1}$

Step 2

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x^{3} - x^{2}) - 24 x + 12}{2 x - 1}$

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

$\frac{x^{2} (2 x - 1) - 12 (2 x - 1)}{2 x - 1}$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$\frac{(2 x - 1) (x^{2} - 12)}{2 x - 1}$

Step 3

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

$\frac{(2 x - 1) (x^{2} - 12)}{2 x - 1}$

Divide $x^{2} - 12$ by $1$ .

$x^{2} - 12$