Precalculus Examples

$a^{2} - 2 a x - 48 x^{2}$

Step 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 $a \cdot c = 1 \cdot - 48 = - 48$ and whose sum is $b = - 2$ .

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Step 1.1

Reorder terms.

$a^{2} - 48 x^{2} - 2 a x$

Step 1.2

Reorder $- 48 x^{2}$ and $- 2 a x$ .

$a^{2} - 2 a x - 48 x^{2}$

Step 1.3

Factor $- 2$ out of $- 2 a x$ .

$a^{2} - 2 (a x) - 48 x^{2}$

Step 1.4

Rewrite $- 2$ as $6$ plus $- 8$

$a^{2} + (6 - 8) (a x) - 48 x^{2}$

Step 1.5

Apply the distributive property.

$a^{2} + 6 (a x) - 8 (a x) - 48 x^{2}$

Step 1.6

Remove unnecessary parentheses.

$a^{2} + 6 a x - 8 (a x) - 48 x^{2}$

Step 1.7

Remove unnecessary parentheses.

$a^{2} + 6 a x - 8 a x - 48 x^{2}$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(a^{2} + 6 a x) - 8 a x - 48 x^{2}$

Step 2.2

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

$a (a + 6 x) - 8 x (a + 6 x)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $a + 6 x$ .

$(a + 6 x) (a - 8 x)$