Factor p(x)=x^3-2x^2-4x^2+8x

$p (x) = x^{3} - 2 x^{2} - 4 x^{2} + 8 x$

Step 1

Subtract $4 x^{2}$ from $- 2 x^{2}$ .

$p (x) = x^{3} - 6 x^{2} + 8 x$

Step 2

Factor $x$ out of $x^{3} - 6 x^{2} + 8 x$ .

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

$p (x) = x \cdot x^{2} - 6 x^{2} + 8 x$

Factor $x$ out of $- 6 x^{2}$ .

$p (x) = x \cdot x^{2} + x (- 6 x) + 8 x$

Factor $x$ out of $8 x$ .

$p (x) = x \cdot x^{2} + x (- 6 x) + x \cdot 8$

Factor $x$ out of $x \cdot x^{2} + x (- 6 x)$ .

$p (x) = x (x^{2} - 6 x) + x \cdot 8$

Factor $x$ out of $x (x^{2} - 6 x) + x \cdot 8$ .

$p (x) = x (x^{2} - 6 x + 8)$

Step 3

Factor.

Factor $x^{2} - 6 x + 8$ 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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$p (x) = x ((x - 4) (x - 2))$

Remove unnecessary parentheses.

$p (x) = x (x - 4) (x - 2)$

Factor p(x)=x^3-2x^2-4x^2+8x

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