thay x = 16, ta có :
16^4-17*16^3+17*16^2-17*16+20
=16^4-17*(16^3-16^2+16)+20
=65536-17*3856+20
=65536-65552+20
=4
theo bài ra ta có:\
\(M=x^4-17x^3+17x^2-17x+20\\ \Rightarrow M=x^4-\left(16x^3+x^3\right)+\left(16x^2+x^2\right)-\left(16x+x\right)+20\\ \Rightarrow M=x^4-16x^3-x^3+16x^2+x^2-16x-x+20\left(1\right)\) thay x = 16 vào 1 ta có:
\(M=x^4-x.x^3-x^3+x.x^2+x^2-x.x-x+20\)
\(\Rightarrow M=x^4-x^4-x^3+x^3+x^2-x^2-x+20\\ \Rightarrow M=-x+20\\ \Rightarrow M=-16+20\\ \Rightarrow M=4\)
vậy M = 4