Factor 10x-3-3x^2

$10 x - 3 - 3 x^{2}$

Step 1

Factor $- 1$ out of $10 x - 3 - 3 x^{2}$ .

Reorder the expression.

Move $- 3$ .

$10 x - 3 x^{2} - 3$

Reorder $10 x$ and $- 3 x^{2}$ .

$- 3 x^{2} + 10 x - 3$

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

$- (3 x^{2}) + 10 x - 3$

Factor $- 1$ out of $10 x$ .

$- (3 x^{2}) - (- 10 x) - 3$

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

$- (3 x^{2}) - (- 10 x) - 1 (3)$

Factor $- 1$ out of $- (3 x^{2}) - (- 10 x)$ .

$- (3 x^{2} - 10 x) - 1 (3)$

Factor $- 1$ out of $- (3 x^{2} - 10 x) - 1 (3)$ .

$- (3 x^{2} - 10 x + 3)$

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 $a \cdot c = 3 \cdot 3 = 9$ and whose sum is $b = - 10$ .

Factor $- 10$ out of $- 10 x$ .

$- (3 x^{2} - 10 (x) + 3)$

Rewrite $- 10$ as $- 1$ plus $- 9$

$- (3 x^{2} + (- 1 - 9) x + 3)$

Apply the distributive property.

$- (3 x^{2} - 1 x - 9 x + 3)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((3 x^{2} - 1 x) - 9 x + 3)$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

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

Remove unnecessary parentheses.

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

Factor 10x-3-3x^2

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