Factor (24x^2+2x-15)/(20x^2-23x+16)

$\frac{24 x^{2} + 2 x - 15}{20 x^{2} - 23 x + 16}$

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 $a \cdot c = 24 \cdot - 15 = - 360$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

$\frac{24 x^{2} + 2 (x) - 15}{20 x^{2} - 23 x + 16}$

Rewrite $2$ as $- 18$ plus $20$

$\frac{24 x^{2} + (- 18 + 20) x - 15}{20 x^{2} - 23 x + 16}$

Apply the distributive property.

$\frac{24 x^{2} - 18 x + 20 x - 15}{20 x^{2} - 23 x + 16}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(24 x^{2} - 18 x) + 20 x - 15}{20 x^{2} - 23 x + 16}$

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

$\frac{6 x (4 x - 3) + 5 (4 x - 3)}{20 x^{2} - 23 x + 16}$

Factor the polynomial by factoring out the greatest common factor, $4 x - 3$ .

$\frac{(4 x - 3) (6 x + 5)}{20 x^{2} - 23 x + 16}$

Factor (24x^2+2x-15)/(20x^2-23x+16)

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