Divide (3x^2-11x-4)/(x-4)

$\frac{3 x^{2} - 11 x - 4}{x - 4}$

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 $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$\frac{3 x^{2} - 11 (x) - 4}{x - 4}$

Rewrite $- 11$ as $1$ plus $- 12$

$\frac{3 x^{2} + (1 - 12) x - 4}{x - 4}$

Apply the distributive property.

$\frac{3 x^{2} + 1 x - 12 x - 4}{x - 4}$

Multiply $x$ by $1$ .

$\frac{3 x^{2} + x - 12 x - 4}{x - 4}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x^{2} + x) - 12 x - 4}{x - 4}$

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

$\frac{x (3 x + 1) - 4 (3 x + 1)}{x - 4}$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$\frac{(3 x + 1) (x - 4)}{x - 4}$

Step 2

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{(3 x + 1) (x - 4)}{x - 4}$

Divide $3 x + 1$ by $1$ .

$3 x + 1$

Divide (3x^2-11x-4)/(x-4)

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