Simplify (3x^2-4x-4)/(6x^3+4x^2+3x+2)

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

Step 1

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

Factor $- 4$ out of $- 4 x$ .

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

Rewrite $- 4$ as $2$ plus $- 6$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 2

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 3

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 2}{2 x^{2} + 1}$

Simplify (3x^2-4x-4)/(6x^3+4x^2+3x+2)

Related Questions

Support LCMGCF.com by disabling your adblocker.