Finite Math Examples

$2 x^{2} - x^{2} - 7 x + 6$

Step 1

Regroup terms.

$- 7 x + 2 x^{2} - x^{2} + 6$

Step 2

Subtract $x^{2}$ from $2 x^{2}$ .

$- 7 x + x^{2} + 6$

Step 3

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$- 7 u + u^{2} + 6$

Step 4

Factor $- 7 u + u^{2} + 6$ using the AC method.

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Step 4.1

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 $- 7$ .

$- 6, - 1$

Step 4.2

Write the factored form using these integers.

$(u - 6) (u - 1)$

Step 5

Replace all occurrences of $u$ with $x$ .

$(x - 6) (x - 1)$