Linear Algebra Examples

$x^{2} - 3 x + 2 = 0$

Step 1

Factor

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

$2$ and whose sum is

$- 3$ .

$- 2, - 1$

Step 1.2

Write the factored form using these integers.

$(x - 2) (x - 1) = 0$

Step 2

If any individual factor on the left side of the equation is equal to

$0$ , the entire expression will be equal to

$0$ .

$x - 2 = 0$

$x - 1 = 0$

Step 3

Set

$x - 2$ equal to

$0$ and solve for

$x$ .

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Step 3.1

Set

$x - 2$ equal to

$0$ .

$x - 2 = 0$

Step 3.2

Add

$2$ to both sides of the equation.

$x = 2$

Step 4

Set

$x - 1$ equal to

$0$ and solve for

$x$ .

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Step 4.1

Set

$x - 1$ equal to

$0$ .

$x - 1 = 0$

Step 4.2

Add

$1$ to both sides of the equation.

$x = 1$

Step 5

The final solution is all the values that make

$(x - 2) (x - 1) = 0$ true.

$x = 2, 1$

Step 6

The domain is the set of all valid

$x$ values.

${x | x = 2, 1}$

Step 7