How do you factor the polynomial 16x^4-81
+245 To factor this polynomial you must first be comfortable with the idea of the difference or squares.
Eg. a^2 - b^2 = (a+b) (a-b)
*This will help you solve the problem*
Now for the problem:
\(16x^4 - 81\)
\((4x^2)^2 - 9^2\)
\(a^2 - b^2 = (a+b)(a-b)\)
Set: a to \(4x^2 \)
b to \(9\)
\((4x^2 + 9) (4x^2-9) \)
Notice that the term on the right side is another difference of squares hence you can factor it even more. The term on the left side can not be factored because it is a sum of squares.
For the term on the right set a to 2x and b to 3
\((4x^2 + 9) (4x^2-9)\)
\((4x^2 + 9) (2x+3)(2x-3)\)
This is your final answer: \((4x^2 + 9) (2x+3)(2x-3)\)
