Therefore, there are two ways to directly decompose cross multiplication:
4x^4- 13x^2+9
=(4x^2- 1)(x^2-9)
=(2x+ 1)(2x- 1)(x+3)(x-3)
Another violent solution, in fact, is to know the four roots of 4x 4- 13x 2+9 = 0, and then multiply it by the highest coefficient, and you can solve it violently:
Let t = x 2, then 4x 4- 13x 2+9 = 0 can be transformed into
4t^2- 13t+9=0
According to the root formula
t =( 13 √( 13^2-4*4*9))/8=( 13 5)/8
That is, x 2 = 9/4 or x 2 = 1.
So x = 3/2 or x = 1.
That is, for the equation 4x 4- 13x 2+9 = 0.
Equivalent to 4 (x+3/2) (x-3/2) (x+1) (x-1) = 0.
Divide 4 by 2 times 2 times the first two brackets, and the result of the first method is the same.