Select the correct choice below.

(a) 9x^3 +72=?

(b) The polynomial is prime.

Select the correct choice below.

(a) 9x^3 +72=?

(b) The polynomial is prime.

Tutors, please sign in to answer this question.

Thisi is about factoring the expresssion

9x^{3} + 72 = 9(x^{3} +8) = 9 (x^{3} +2^{3}) = 9(x+2)(x^{2} - 2x +4)

If you have to solve the equation 9x^{3} + 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

x^{2} -2x +4 = 0 or x^{2} - 2x + 1 = -3

Thus (x-1)^{ 2} = -3 and solutions are x_{ 1} = 1 + √3 i and x_{2} = 1 - √3 i

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!

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