Precalculus Examples

$x^{2} + x y + 3 x + 2 y + 2$

Step 1

Regroup terms.

$x y + 2 y + x^{2} + 3 x + 2$

Step 2

Factor $y$ out of $x y + 2 y$ .

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Step 2.1

Factor $y$ out of $x y$ .

$y x + 2 y + x^{2} + 3 x + 2$

Step 2.2

Factor $y$ out of $2 y$ .

$y x + y \cdot 2 + x^{2} + 3 x + 2$

Step 2.3

Factor $y$ out of $y x + y \cdot 2$ .

$y (x + 2) + x^{2} + 3 x + 2$

Step 3

Factor $x^{2} + 3 x + 2$ using the AC method.

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Step 3.1

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 $2$ and whose sum is $3$ .

$1, 2$

Step 3.2

Write the factored form using these integers.

$y (x + 2) + (x + 1) (x + 2)$

Step 4

Factor $x + 2$ out of $y (x + 2) + (x + 1) (x + 2)$ .

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Step 4.1

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

$(x + 2) y + (x + 1) (x + 2)$

Step 4.2

Factor $x + 2$ out of $(x + 1) (x + 2)$ .

$(x + 2) y + (x + 2) (x + 1)$

Step 4.3

Factor $x + 2$ out of $(x + 2) y + (x + 2) (x + 1)$ .

$(x + 2) (y + x + 1)$