Andrew M. answered • 04/21/16

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

It appears that Roman C made an error in

factoring the polynomial:

64x

^{3}+ 8 = 064x

^{3}= -8x

^{3}= -8/64x

^{3}= -1/8**x = -1/2**

This is the real root

Since x=-1/2 is a root then (x+1/2) is a factor

64x

^{3}+ 8 = (x+1/2)(___??____) = 0Using synthetic division I can find the missing factor

-1/2 | 64 0 0 8

| -32 16 -8

--------------------

64 -32 16 0

The polynomial we get in factoring out (x+1/2) is

64x

^{3}+ 8 = (x+1/2)(64x^{2}- 32x + 16)Note that we can factor 16 out of each term in the 2nd polymomial

(16)(x+1/2)(4x

^{2}- 2x + 1) = 0Divide both sides by 16

(x+1/2)(4x

^{2}- 2x + 1) = 0We already know that x=-1/2 is a root.

We need to find the roots of 4x

^{2}-2x+1=0Using quadratic equation

x =[ -b ±√(b

^{2}-4ac)]/2a a=4, b=-2, c=1x = [2 ±√[(-2)

^{2}-4(4)(1)]]/2(4)x = (2±√(4-16))/8

x = (2±√-12)/8

x = (2±2i√3)/8

x = (1 ± i√3)/4

**x = 1/4 ± (√3/4)i**

Due to the dropping of the negative sign on his factoring,

Roman C. had -1/4 instead of 1/4 in the final answer

Malik D.

04/21/16