Solve by Factoring 2x^3-18x^2-8x+72=0

$2 x^{3} - 18 x^{2} - 8 x + 72 = 0$

Step 1

Factor $2$ out of $2 x^{3} - 18 x^{2} - 8 x + 72$ .

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

$2 (x^{3}) - 18 x^{2} - 8 x + 72 = 0$

Factor $2$ out of $- 18 x^{2}$ .

$2 (x^{3}) + 2 (- 9 x^{2}) - 8 x + 72 = 0$

Factor $2$ out of $- 8 x$ .

$2 (x^{3}) + 2 (- 9 x^{2}) + 2 (- 4 x) + 72 = 0$

Factor $2$ out of $72$ .

$2 x^{3} + 2 (- 9 x^{2}) + 2 (- 4 x) + 2 \cdot 36 = 0$

Factor $2$ out of $2 x^{3} + 2 (- 9 x^{2})$ .

$2 (x^{3} - 9 x^{2}) + 2 (- 4 x) + 2 \cdot 36 = 0$

Factor $2$ out of $2 (x^{3} - 9 x^{2}) + 2 (- 4 x)$ .

$2 (x^{3} - 9 x^{2} - 4 x) + 2 \cdot 36 = 0$

Factor $2$ out of $2 (x^{3} - 9 x^{2} - 4 x) + 2 \cdot 36$ .

$2 (x^{3} - 9 x^{2} - 4 x + 36) = 0$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((x^{3} - 9 x^{2}) - 4 x + 36) = 0$

Factor out the greatest common factor (GCF) from each group.

$2 (x^{2} (x - 9) - 4 (x - 9)) = 0$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 9$ .

$2 ((x - 9) (x^{2} - 4)) = 0$

Step 4

Rewrite $4$ as $2^{2}$ .

$2 ((x - 9) (x^{2} - 2^{2})) = 0$

Step 5

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$2 ((x - 9) ((x + 2) (x - 2))) = 0$

Remove unnecessary parentheses.

$2 ((x - 9) (x + 2) (x - 2)) = 0$

Remove unnecessary parentheses.

$2 (x - 9) (x + 2) (x - 2) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 9 = 0$

$x + 2 = 0$

$x - 2 = 0$

Step 7

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 8

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 9

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 10

The final solution is all the values that make $2 (x - 9) (x + 2) (x - 2) = 0$ true.

$x = 9, - 2, 2$

Solve by Factoring 2x^3-18x^2-8x+72=0

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