Find the values of a and b so that(x-1) and (x+1) are the factors of x⁴+ax³-3x²+2x+b

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Solution

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

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