Kindly proofread the question!!!
The leading term is x^6, not x5.
Answer: The additional roots are -2, +2, each with multiplicity 2.
Step-by-step explanation:
x^6 - 16x^2 = 4x^4 - 64
x^6 - 4x^4 - 16x^2 + 64 = 0
(x+2i)(x-2i) = (x^2+4) is a factor.
(x-2)(x+2)(x-2)(x+2)(x^2+4) = 0
Polynomial long division by x^2+4
x^6 - 4x^4 - 16x^2 + 64 = 0
First term of quotient is x^4
Subtract x^6+4x^4
Remainder is -8x^4 -16x^2+64
Second quotient term is -8x^2
Subtract -8x^4-32x^2
Remainder is 16x^2+64
Third quotient term is 16
Subtract 16x^2+64
Remainder is zero
Quotient is x^4 - 8x^2 + 16
(x^2-4)^2 = x^4 + 2(1)(-4)x^2 + 16
(x-2)(x+2)(x-2)(x+2)(x^2+4) = 0
