Factor x^4-4x^3+3x^2

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

Step 1

Factor $x^{2}$ out of $x^{4} - 4 x^{3} + 3 x^{2}$ .

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

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

Factor $x^{2}$ out of $- 4 x^{3}$ .

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

Factor $x^{2}$ out of $3 x^{2}$ .

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

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

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

Factor $x^{2}$ out of $x^{2} (x^{2} - 4 x) + x^{2} \cdot 3$ .

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

Step 2

Factor.

Factor $x^{2} - 4 x + 3$ using the AC method.

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 $3$ and whose sum is $- 4$ .

$- 3, - 1$

Write the factored form using these integers.

$x^{2} ((x - 3) (x - 1))$

Remove unnecessary parentheses.

$x^{2} (x - 3) (x - 1)$

Factor x^4-4x^3+3x^2

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