Simplify (9-4k)/(3k^2+13k+4)

$\frac{9 - 4 k}{3 k^{2} + 13 k + 4}$

Step 1

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 $b = 13$ .

Factor $13$ out of $13 k$ .

$\frac{9 - 4 k}{3 k^{2} + 13 (k) + 4}$

Rewrite $13$ as $1$ plus $12$

$\frac{9 - 4 k}{3 k^{2} + (1 + 12) k + 4}$

Apply the distributive property.

$\frac{9 - 4 k}{3 k^{2} + 1 k + 12 k + 4}$

Multiply $k$ by $1$ .

$\frac{9 - 4 k}{3 k^{2} + k + 12 k + 4}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{9 - 4 k}{(3 k^{2} + k) + 12 k + 4}$

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

$\frac{9 - 4 k}{k (3 k + 1) + 4 (3 k + 1)}$

Step 3

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

$\frac{9 - 4 k}{(3 k + 1) (k + 4)}$

Simplify (9-4k)/(3k^2+13k+4)

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