Algebra Examples

$- 4 x^{2} - x + 5$

Step 1

Factor $- 1$ out of $- 4 x^{2} - x + 5$ .

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Step 1.1

Factor $- 1$ out of $- 4 x^{2}$ .

$- (4 x^{2}) - x + 5$

Step 1.2

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

$- (4 x^{2}) - (x) + 5$

Step 1.3

Rewrite $5$ as $- 1 (- 5)$ .

$- (4 x^{2}) - (x) - 1 (- 5)$

Step 1.4

Factor $- 1$ out of $- (4 x^{2}) - (x)$ .

$- (4 x^{2} + x) - 1 (- 5)$

Step 1.5

Factor $- 1$ out of $- (4 x^{2} + x) - 1 (- 5)$ .

$- (4 x^{2} + x - 5)$

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 $a \cdot c = 4 \cdot - 5 = - 20$ and whose sum is $b = 1$ .

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Step 2.1.1.1

Multiply by $1$ .

$- (4 x^{2} + 1 x - 5)$

Step 2.1.1.2

Rewrite $1$ as $- 4$ plus $5$

$- (4 x^{2} + (- 4 + 5) x - 5)$

Step 2.1.1.3

Apply the distributive property.

$- (4 x^{2} - 4 x + 5 x - 5)$

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.

$- ((4 x^{2} - 4 x) + 5 x - 5)$

Step 2.1.2.2

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

$- (4 x (x - 1) + 5 (x - 1))$

Step 2.1.3

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

$- ((x - 1) (4 x + 5))$

Step 2.2

Remove unnecessary parentheses.

$- (x - 1) (4 x + 5)$