Factor 8x^2-22x+15

$8 x^{2} - 22 x + 15$

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 $a \cdot c = 8 \cdot 15 = 120$ and whose sum is $b = - 22$ .

Factor $- 22$ out of $- 22 x$ .

$8 x^{2} - 22 (x) + 15$

Rewrite $- 22$ as $- 10$ plus $- 12$

$8 x^{2} + (- 10 - 12) x + 15$

Apply the distributive property.

$8 x^{2} - 10 x - 12 x + 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} - 10 x) - 12 x + 15$

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

$2 x (4 x - 5) - 3 (4 x - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 5$ .

$(4 x - 5) (2 x - 3)$

Factor 8x^2-22x+15

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