a, \(P\left(x\right)=x^7-80x^6+80x^5-....+80x+15\)
\(P\left(x\right)=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-...+\left(x+1\right)x+15\)
\(P\left(x\right)=x^7-x^7-x^6+x^6+x^5-.....-x^3-x^2+x^2+x+15\)
\(P\left(x\right)=x+15\)(1)
Thay \(x=79\) vào (1) ta được: \(79+15=84\)
b, \(R\left(x\right)=x^4-17x^3+17x^2-17x+20\)
\(R\left(x\right)=x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+20\)
\(R\left(x\right)=x^4-x^4-x^3+x^3+x^2-x^2-x+20\)
\(R\left(x\right)=-x+20\)(2)
Thay \(x=16\) vào (2) ta được: \(-16+20=4\)
Chúc bạn học tốt!!!
\(\text{P(x)}=x^7-80x^6+80x^5-80x^4+...+80x+15\)
=\(x^7-79x^6-x^6+79x^5-...-x^2+79x+x+15\)
=\(\left(x^6-x^5+...-x\right)\left(x-79\right)+x+15\)
=\(0+79+15=94\)
\(R\left(x\right)=x^4-17x^3+17x^2-17x+20\)
=\(x^4-16x^3-x^3+16x^2+x^2-16x-x+20\)
=\(\left(x^3-x^2+x\right)\left(x-16\right)-\left(x-20\right)\)
=\(0-\left(16-20\right)=4\)
