Divide (8x+4+3x^2)/(3x+2)

$\frac{8 x + 4 + 3 x^{2}}{3 x + 2}$

Step 1

Factor by grouping.

Reorder terms.

$\frac{3 x^{2} + 8 x + 4}{3 x + 2}$

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 $a \cdot c = 3 \cdot 4 = 12$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$\frac{3 x^{2} + 8 (x) + 4}{3 x + 2}$

Rewrite $8$ as $2$ plus $6$

$\frac{3 x^{2} + (2 + 6) x + 4}{3 x + 2}$

Apply the distributive property.

$\frac{3 x^{2} + 2 x + 6 x + 4}{3 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x^{2} + 2 x) + 6 x + 4}{3 x + 2}$

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

$\frac{x (3 x + 2) + 2 (3 x + 2)}{3 x + 2}$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$\frac{(3 x + 2) (x + 2)}{3 x + 2}$

Step 2

Cancel the common factor of $3 x + 2$ .

Cancel the common factor.

$\frac{(3 x + 2) (x + 2)}{3 x + 2}$

Divide $x + 2$ by $1$ .

$x + 2$

Divide (8x+4+3x^2)/(3x+2)

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