Factor -2x^2+7x-3

$- 2 x^{2} + 7 x - 3$

Step 1

Factor $- 1$ out of $- 2 x^{2} + 7 x - 3$ .

Factor $- 1$ out of $- 2 x^{2}$ .

$- (2 x^{2}) + 7 x - 3$

Factor $- 1$ out of $7 x$ .

$- (2 x^{2}) - (- 7 x) - 3$

Rewrite $- 3$ as $- 1 (3)$ .

$- (2 x^{2}) - (- 7 x) - 1 (3)$

Factor $- 1$ out of $- (2 x^{2}) - (- 7 x)$ .

$- (2 x^{2} - 7 x) - 1 (3)$

Factor $- 1$ out of $- (2 x^{2} - 7 x) - 1 (3)$ .

$- (2 x^{2} - 7 x + 3)$

Step 2

Factor.

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$- (2 x^{2} - 7 (x) + 3)$

Rewrite $- 7$ as $- 1$ plus $- 6$

$- (2 x^{2} + (- 1 - 6) x + 3)$

Apply the distributive property.

$- (2 x^{2} - 1 x - 6 x + 3)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((2 x^{2} - 1 x) - 6 x + 3)$

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

$- (x (2 x - 1) - 3 (2 x - 1))$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$- ((2 x - 1) (x - 3))$

Remove unnecessary parentheses.

$- (2 x - 1) (x - 3)$

Factor -2x^2+7x-3

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