is x-(a+b) factor of x⁴-4abx²-(a²-b²)²?
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p(x)=x^4-4abx^2 -(a^2-b^2)^2
g (x)=x-(a+b)=x-a-b = x=a+b
by factor theorem,
p (a+b) = (a+b)^4 -4×ab(a+b)^2 -(a^2-b^2)^2
(a^4+b^4) - 4×ab (a^2 + b^2)-(a^4-b^4)
-4a^3×b-4ab^3
remainder is not 0 therefore, it is not the factor
g (x)=x-(a+b)=x-a-b = x=a+b
by factor theorem,
p (a+b) = (a+b)^4 -4×ab(a+b)^2 -(a^2-b^2)^2
(a^4+b^4) - 4×ab (a^2 + b^2)-(a^4-b^4)
-4a^3×b-4ab^3
remainder is not 0 therefore, it is not the factor
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