Factor 7x^2-19x+10

$7 x^{2} - 19 x + 10$

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 $a \cdot c = 7 \cdot 10 = 70$ and whose sum is $b = - 19$ .

Factor $- 19$ out of $- 19 x$ .

$7 x^{2} - 19 (x) + 10$

Rewrite $- 19$ as $- 5$ plus $- 14$

$7 x^{2} + (- 5 - 14) x + 10$

Apply the distributive property.

$7 x^{2} - 5 x - 14 x + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 5 x) - 14 x + 10$

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

$x (7 x - 5) - 2 (7 x - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 5$ .

$(7 x - 5) (x - 2)$

Factor 7x^2-19x+10

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