Calculus Examples

$2 + 7 x - 4 x^{2}$

Step 1

Factor $- 1$ out of $2 + 7 x - 4 x^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $2$ .

$7 x - 4 x^{2} + 2$

Step 1.1.2

Reorder $7 x$ and $- 4 x^{2}$ .

$- 4 x^{2} + 7 x + 2$

Step 1.2

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

$- (4 x^{2}) + 7 x + 2$

Step 1.3

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

$- (4 x^{2}) - (- 7 x) + 2$

Step 1.4

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

$- (4 x^{2}) - (- 7 x) - 1 (- 2)$

Step 1.5

Factor $- 1$ out of $- (4 x^{2}) - (- 7 x)$ .

$- (4 x^{2} - 7 x) - 1 (- 2)$

Step 1.6

Factor $- 1$ out of $- (4 x^{2} - 7 x) - 1 (- 2)$ .

$- (4 x^{2} - 7 x - 2)$

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 $a \cdot c = 4 \cdot - 2 = - 8$ and whose sum is $b = - 7$ .

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Step 2.1.1.1

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

$- (4 x^{2} - 7 (x) - 2)$

Step 2.1.1.2

Rewrite $- 7$ as $1$ plus $- 8$

$- (4 x^{2} + (1 - 8) x - 2)$

Step 2.1.1.3

Apply the distributive property.

$- (4 x^{2} + 1 x - 8 x - 2)$

Step 2.1.1.4

Multiply $x$ by $1$ .

$- (4 x^{2} + x - 8 x - 2)$

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.

$- ((4 x^{2} + x) - 8 x - 2)$

Step 2.1.2.2

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

$- (x (4 x + 1) - 2 (4 x + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$- ((4 x + 1) (x - 2))$

Step 2.2

Remove unnecessary parentheses.

$- (4 x + 1) (x - 2)$