Factor the expression completely.

Question

Select the correct choice below.

(a) 9x^3 +72=?

(b) The polynomial is prime.

Answer 1

Thisi is about factoring the expresssion 

9x³ + 72 = 9(x³ +8) = 9 (x³ +2³) = 9(x+2)(x² - 2x +4)

If you have to solve the equation 9x³ + 72 = 0 then one of solutions is x = -2    because  we can put x+2 =0 as one of factors.

Two other solutions (you should have three because you have a cubic equation) are complex conjugates of the quadratic equation

                                               x² -2x +4 = 0       or  x² - 2x + 1 = -3

Thus        (x-1) ² = -3           and solutions are   x ₁ = 1 + √3 i      and  x₂ = 1 - √3 i

 

Answer 2

Begin by rearranging the equation by subtracting 72 from both sides:  9x^3=-72.

Next, divide both sides of the equation by 9:( 9x^3)/9=-72/9 --->x^3=-8.

Finally, take the cube root of both sides: (x^3)^(1/3)=(-8)^3--->x=-2.

Hope this helps!