Linear Algebra Examples

$(x - 3 x^{2} + 2) \div (x - 3)$

Step 1

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

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Step 1.1

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

$(- 3 x^{2} + x + 2) \div (x - 3)$

Step 1.2

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

$(- (3 x^{2}) + x + 2) \div (x - 3)$

Step 1.3

Factor $- 1$ out of $x$ .

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

Step 1.4

Rewrite $2$ as $- 1 (- 2)$ .

$(- (3 x^{2}) - 1 (- x) - 1 (- 2)) \div (x - 3)$

Step 1.5

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

$(- (3 x^{2} - x) - 1 (- 2)) \div (x - 3)$

Step 1.6

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

$- (3 x^{2} - x - 2) \div (x - 3)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = - 1$ .

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Step 2.1.1.1

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

$- (3 x^{2} - (x) - 2) \div (x - 3)$

Step 2.1.1.2

Rewrite $- 1$ as $2$ plus $- 3$

$- (3 x^{2} + (2 - 3) x - 2) \div (x - 3)$

Step 2.1.1.3

Apply the distributive property.

$- (3 x^{2} + 2 x - 3 x - 2) \div (x - 3)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$- ((3 x^{2} + 2 x) - 3 x - 2) \div (x - 3)$

Step 2.1.2.2

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

$- (x (3 x + 2) - (3 x + 2)) \div (x - 3)$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$- ((3 x + 2) (x - 1)) \div (x - 3)$

Step 2.2

Remove unnecessary parentheses.

$- (3 x + 2) (x - 1) \div (x - 3)$