3x^3-x^2-27x+9

Question

solutions by factoring.

Answer 1

The polynomial is 3x ³ - x ² - 27x + 9

Take out common factors.

= x ²(3x - 1) - 9(3x - 1)

= (3x - 1)(x ² - 9)

= (3x - 1)(x ² - 9)

To solve the polynomial (3x - 1)(x ² - 9) = 0.

Apply zero product property.

3x - 1 = 0 and  x ² - 9 = 0

3x - 1 = 0

3x = 1

x  = 1/3

Now x ² - 9 = 0

From (a +b )(a - b ) = a ² - b ².

(x + 3)(x - 3) = 0

(x + 3) = 0 and (x - 3) = 0

x = - 3 and x = 3

Solutions are x = 3 , -3 and 1/3.