Calculus Examples

$12 x^{2} - 176 x + 484$

Step 1

Factor out the GCF of $4$ from $12 x^{2} - 176 x + 484$ .

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Step 1.1

Factor out the GCF of $4$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $4$ from the expression $12 x^{2}$ .

$4 (3 x^{2}) - 176 x + 484$

Step 1.1.2

Factor out the GCF of $4$ from the expression $- 176 x$ .

$4 (3 x^{2}) + 4 (- 44 x) + 484$

Step 1.1.3

Factor out the GCF of $4$ from the expression $484$ .

$4 (3 x^{2}) + 4 (- 44 x) + 4 (121)$

Step 1.2

Since all the terms share a common factor of $4$ , it can be factored out of each term.

$4 (3 x^{2} - 44 x + 121)$

Step 2

Factor by grouping.

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Step 2.1

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 $a \cdot c = 3 \cdot 121 = 363$ and whose sum is $b = - 44$ .

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Step 2.1.1

Factor $- 44$ out of $- 44 x$ .

$4 (3 x^{2} - 44 x + 121)$

Step 2.1.2

Rewrite $- 44$ as $- 11$ plus $- 33$

$4 (3 x^{2} + (- 11 - 33) x + 121)$

Step 2.1.3

Apply the distributive property.

$4 (3 x^{2} - 11 x - 33 x + 121)$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$4 ((3 x^{2} - 11 x) - 33 x + 121)$

Step 2.2.2

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

$4 (x (3 x - 11) - 11 (3 x - 11))$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $3 x - 11$ .

$4 ((3 x - 11) (x - 11))$