Divide (6a^2+a-2)÷(2a-1)

$(6 a^{2} + a - 2) \div (2 a - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{6 a^{2} + a - 2}{2 a - 1}$

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot - 2 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

$\frac{6 a^{2} + 1 a - 2}{2 a - 1}$

Rewrite $1$ as $- 3$ plus $4$

$\frac{6 a^{2} + (- 3 + 4) a - 2}{2 a - 1}$

Apply the distributive property.

$\frac{6 a^{2} - 3 a + 4 a - 2}{2 a - 1}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 a^{2} - 3 a) + 4 a - 2}{2 a - 1}$

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

$\frac{3 a (2 a - 1) + 2 (2 a - 1)}{2 a - 1}$

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

$\frac{(2 a - 1) (3 a + 2)}{2 a - 1}$

Step 3

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

Cancel the common factor.

$\frac{(2 a - 1) (3 a + 2)}{2 a - 1}$

Divide $3 a + 2$ by $1$ .

$3 a + 2$

Divide (6a^2+a-2)÷(2a-1)

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