Question

a) 4x^4 +81

b)x^8 +9x^4 +1

Answer 1

a) \(4x^4+81=\left[\left(2x^2\right)^2+36x^2+9^2\right]-36x^2=\left(2x^2+9\right)-\left(6x\right)^2=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)

b) \(x^8+9x^4+1=\left[\left(x^4\right)^2+2x^4+1\right]-7x^4=\left(x^4+1\right)-\left(\sqrt{7}x^2\right)^2=\left(x^4+1-\sqrt{7}\right)\left(x^4+1+\sqrt{7}\right)\)