因式分解x15+x14+x13+…+x2+x+1 要过程

2024-12-19 05:52:38
推荐回答(1个)
回答1:

=X14(X+1)+X12(X+1)+X10(X+1)+X8(X+1)+X6(X+1)+X4(X+1)+X2(X+1)+(X+1)
=(X14+X12+X10+X8+X6+X4+X2+1)(X+1)
=[X12(X2+1)+X8(X2+1)+X6(X2+1)+X4(X2+1)+X2(X2+1)](X+1)
=(X12+X8+X4+1)(X2+1)(X+1)
=(X8+1)(X4+1)(X2+1)(X+1)