Question

find the other zeros of the polynomial x⁴ -1 it two zeros are 1,-1​

Answer 1

P(x) = (x-2) (2x^2 + x-2 ) - 1

CHECK: Divide P(x) by (x-2);

quotient is (x-2) (2x^2 + x-2 ) / (x-2) or (2x^2 + x-2 )

Remainder: -1

Simplify:

P(x) = (x-2) (2x^2 + x-2 ) - 1

= x(2x^2) + x(x) + x(-2) - 2(2x^2) - 2(x) -2(-2) - 1

= 2x^3 + x^2 - 2x - 4x^2 - 2x + 4 - 1

= 2x^3 - 3x^2 - 4x + 3