Calculus Examples

$- 3 x^{2} + 8 x + 16$

Step 1

Factor $- 1$ out of $- 3 x^{2} + 8 x + 16$ .

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Step 1.1

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

$- (3 x^{2}) + 8 x + 16$

Step 1.2

Factor $- 1$ out of $8 x$ .

$- (3 x^{2}) - (- 8 x) + 16$

Step 1.3

Rewrite $16$ as $- 1 (- 16)$ .

$- (3 x^{2}) - (- 8 x) - 1 (- 16)$

Step 1.4

Factor $- 1$ out of $- (3 x^{2}) - (- 8 x)$ .

$- (3 x^{2} - 8 x) - 1 (- 16)$

Step 1.5

Factor $- 1$ out of $- (3 x^{2} - 8 x) - 1 (- 16)$ .

$- (3 x^{2} - 8 x - 16)$

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 $a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is $b = - 8$ .

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Step 2.1.1.1

Factor $- 8$ out of $- 8 x$ .

$- (3 x^{2} - 8 (x) - 16)$

Step 2.1.1.2

Rewrite $- 8$ as $4$ plus $- 12$

$- (3 x^{2} + (4 - 12) x - 16)$

Step 2.1.1.3

Apply the distributive property.

$- (3 x^{2} + 4 x - 12 x - 16)$

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.

$- ((3 x^{2} + 4 x) - 12 x - 16)$

Step 2.1.2.2

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

$- (x (3 x + 4) - 4 (3 x + 4))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 x + 4$ .

$- ((3 x + 4) (x - 4))$

Step 2.2

Remove unnecessary parentheses.

$- (3 x + 4) (x - 4)$