Algebra Examples

$(x^{2} + x - 6) (2 x^{2} + 4 x)$

Step 1

Factor $x^{2} + x - 6$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 1.2

Write the factored form using these integers.

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

Step 2

Factor.

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Step 2.1

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

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Step 2.1.1

Factor $2 x$ out of $2 x^{2}$ .

$(x - 2) (x + 3) (2 x (x) + 4 x)$

Step 2.1.2

Factor $2 x$ out of $4 x$ .

$(x - 2) (x + 3) (2 x (x) + 2 x (2))$

Step 2.1.3

Factor $2 x$ out of $2 x (x) + 2 x (2)$ .

$(x - 2) (x + 3) (2 x (x + 2))$

Step 2.2

Remove unnecessary parentheses.

$(x - 2) (x + 3) \cdot 2 x (x + 2)$