How do you factor #2n^4 - 9n^2 +4 = 0#?
Start by noticing that there are no
If we are looking for integer factorisations, we immediately know
Multiply this out:
We now known that
So our quadratic factorisation is
Can we factor this further? Yes. The second bracket is a difference of two squares,
The question doesn't ask it, but if we wish to solve this equation, then the four quartic roots are immediately available:
It is good practice to verify that each of these is in fact a solution to the original equation.
Re-Write the given equation as follows:
Step 1: Trying to factor by splitting the middle term
Find two factors of
Step 2: Rewrite the polynomial splitting the middle term using the two factors found in step 1 above,
Pulling out the common factors