a) 4x2 - 17xy + 13y2
=4x2-4xy-13xy+13y2
=4x(x-y)-13y(x-y)
=(x-y)(4x-13y)
b) x8 + x4 +1
=x8+2x4+1-x4
=(x4+1)2-x4
=(x4+1-x2)(x4+1+x2)
\(x^8+x^4+1\)
\(=x^8+2x^4+1-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x^4-x^2+1\right)\)