Question

find the value of A and B so that X + 1 and X + X - 1 are the factors of X ^ 4 + X ^ 3 - 3 x ^ 2 + 2 X + b​

Answer 1

Answer:

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Step-by-step explanation:

x4 + ax3 - 3x2 + 2x + b

 

If we know our two factors, then we know our zeros.  Our zeros are -1 and 1.  What we can do is plug in x=-1 into the polynomial and set it equal to zero.  Then we do the same for x=1.

 

1 - a - 3 - 2 + b = 0     --->   for   x=-1

-a + b = 4                      

 

 

1 + a - 3 + 2 + b = 0   --->    for   x=1

 

a + b = 0

 

 

Now we have a system of equations to work with.

 

-a + b = 4                       eq1

a + b = 0                        eq2

 

 

Add the two equations to eliminate the a terms.

 

2b = 4

 

 b = 2

 

 

Substitute this value of b into any of the equations to solve for a.

 

 a = -2