This equation is actually just a quadratic equation because the exponent is a multiple of 2. We could rewrite this equation as a quadratic equation by making the first term a square, the second term a power of one and the third term a constant.
x^4 - 17x^2 + 16=0
(x^2)^2 - 17(x)^2 + 16 =0
Since the equation is now quadratic we can factor it just as we would a quadratic equation.
The factors of 16 that add together to get 17 are 16 and 1.
(x^2 - 16) (X^2-1) =0 It is x^2 because it was x^4
and x^2 times x^2 is x^4.
These are both differences of two squares.
(x-4)(x+4)(x-1)(x+1)=0 Set them equal to 0.
x-4=0 x+4=0 x-1=0 x+1=0 Solve for x.
x=4 x=-4 x=1 x=-1
These four numbers are your answers. Since the degree of this equation was 4, you can get up to 4 answers although some may be imaginary.

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