You want to factor (x4 -91)
First notice that the factors of 91 are 1, 7, 13, and 91.
If we try them all , we see that x4 -91 is a prime polynomial.
Even though the polynomial is prime, that is cannot be factored over the set of rational numbers, it is factorable over the set of Irrational Numbers.
x4 - 91
= (x2)2 - (√91)2
= (x2 - √91)(x2 + √91)
= [x2 - (√√91)2](x2 + √91)
= (x - √√91)(x + √√91)(x2 + √91)
It is: (x-y)4
(x2 + 1)(x2 - 2)
2x to the fourth power minus 162 equals -146
x^2(x - 4)(x + 4)
x cubed minus 216
No.
(3x^2 - 4y^2)(3x^2 + 4y^2)
x^2(1 - x)(1 + x)
So x4 - 1 is the difference of squares, so x4 - 1 = (x2 - 1)(x2 + 1) = (x + 1)(x - 1)(x2 + 1).
Factor x4 - 81. Step 1: both numbers have square roots and have a minus sign between them so the first factor result is (x2+9)(x2-9). Step 2: (x2+9) does not factor, but (x2-9) factors to (x+3)(x-3). Step 3: Solution is (x2+9)(x+3)(x-3).
3(x - 2)(x + 2)(x^2 + 4)
(x4 - 16) = (x2 + 4) (x2 - 4) = (x2 + 4) (x + 2) (x - 2)