Find all rational zeros of the polynomial, and write the polynomial in factored form. P(x)=4x^{4}-37x^{2}+9

Step 1
Given, ${\displaystyle P\left(x\right)=4x^4-37x^2+9}$
For zeroes, substituting,P(x)=0
${\displaystyle \Rightarrow 4x^4-37x^2+9=0}$
${\displaystyle \Rightarrow 4x^4-36x^2-x^2+9=0}$
${\displaystyle \Rightarrow 4x^2(x^2-9)-(x^2-9)=0}$
${\displaystyle \Rightarrow (x^2-9)(4x^2-1)=0}$
${\displaystyle \Rightarrow (x^2-3^2)({\left(2x\right)}^2-1)=0}$
${\displaystyle \Rightarrow (x+3)(x-3)(2x+1)(2x-1)=0}$
${\displaystyle (Using,(a^2-b^2)=(a+b)(a-b))}$
${\displaystyle \Rightarrow (x+3)=0}$, or, (x-3)=0, or , (2x+1)=0, or, (2x-1)=0
${\displaystyle \Rightarrow x=-3,3,-\frac{1}{2},\frac{1}{2}}$
Hence, zeroes are: ${\displaystyle x=(-3,-\frac{1}{2},\frac{1}{2},3)}$.
Step 2
Required factorized form is:
${\displaystyle 4x^4-37x^2+9=(x+3)(x-3)(2x+1)(2x-1)}$