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Help.

NotSoSmart  Nov 20, 2017
 #1
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+2

1.   4x3 + 8x2 - 96x

                                      Factor  4x  out of each term.

=    4x(x2 + 2x - 24)

                                      Factor  x2 + 2x - 24  as  (x - 4)(x + 6) .

=  4x(x - 4)(x + 6)

 

(The one you have selected is right.  smiley  )

 

3.     We want to solve this equation for  x :

 

0  =  x4 - 4x3 + 3x2

                                      Factor  x2  out of all the terms on the right side.

0  =  x2(x2 - 4x + 3)

                                      Factor  x2 - 4x + 3  as  (x - 1)(x - 3) .

0  =  x2(x - 1)(x - 3)

                                      And we can "factor"  x2  as  x * x .

0  =  (x)(x)(x - 1)(x - 3)

                                      Set each factor equal to zero and solve for  x .

 

x  =  0       or       x  =  0       or       x  =  1       or       x  =  3

 

x  =  0  occurs twice, so it has multiplicity  2 .

x  =  1  occurs once, so it has multiplicity  1 .

x  =  3  occurs once, so it has multiplicity  1 .

hectictar  Nov 20, 2017
edited by hectictar  Nov 20, 2017

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