How do you factor #z^4 - 10z^2 + 9#?
1 Answer
Sep 2, 2016
Explanation:
The difference of square identity can be written:
#a^2-b^2=(a-b)(a+b)#
We will use this a couple of times.
Let us treat this as a quadratic in
#z^4-10z^2+9 = (z^2)^2-10(z^2)-9#
#color(white)(z^4-10z^2+9) = (z^2-1)(z^2-9)#
#color(white)(z^4-10z^2+9) = (z^2-1^2)(z^2-3^2)#
#color(white)(z^4-10z^2+9) = (z-1)(z+1)(z-3)(z+3)#