if (x+1) and (x-1) are the factors of the polynomial ax³+x²-2x+b
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here is ur answer ❤️
(x-1) and (x+1) are factors of the given polynomial.
(x-1) = 0 → x=1
(x+1) = 0 → x= -1
Put x = 1
ax³+x²-2x+b
a(1)³+(1)²-2(1)+b = 0
a(1)+1-2+b = 0
a-1+b = 0
a+b = 1 -----(1)
Put x = -1
a(-1)³+(-1)²-2(-1)+b = 0
a(-1)+1+2+b = 0
-a+3+b = 0
-a+b = -3 -----(2)
(1)+(2)
a+b = 1
-a+b = -3
-------------
2b = -2
b = -2/2 = -1
a+b = 1
a+(-1) = 1
a = 1+1
a = 2
Therefore,a = 2 and b = -1
The given polynomial is
2x³+x²-2x+(-1)
2x³+x²-2x-1
Let the third zero be 'q'
Sum of zeroes = -1+1+p = p = -coefficient of x²/coefficient of x³
p = -1/2
Therefore, the third factor = (x+1/2)
thank my answer ❤️
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