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Factor the expression completely.

Select the correct choice below.

(a) 9x^3 +72=?

(b) The polynomial is prime.

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
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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

David M. | Dave "The Math Whiz"Dave "The Math Whiz"
4.8 4.8 (122 lesson ratings) (122)
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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!