Chung minh rang da thuc \(x^{95}+x^{94}+x^{93}+...+x^2+x+1\) chia het cho da thuc \(x^{31}+x^{30}+...+x^2+x+1\)

Da thuc P(x) chia cho x-2 thi du 5 chia cho x-3 thi du 7. tim phan du khi chia P(x) cho (x-2)(x-3)

Tim GTNN cua P :

P=\(x^4-8x^3+27x^2-44x+23\)

Phan tich da thuc thanh nhan tu :

A=\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2\)

phan tich da thuc thanh nhan tu

\(\left(x^2-8\right)^2+36\)

Phan tich da thuc thanh nhan tu

M=\(a\left(b^2-c^2\right)+b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)

Tim x sao cho:

\(1+6x-6x^2-x^3=0\)