Question

which of the following is not a zero of the polynomial x3-6x2+11x-6​

Answer 1

Step-by-step explanation:

⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⢀⣾⣿⣿⣿⠿⠿⠟⠻⠿⢿⣿⣿⣿⡆ ⠀⠀⠀⢰⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇ ⠀⠀⠀⠈⠿⣿⣇⣠⠤⠤⠤⢤⣀⣤⠤⠤⣺⡏ ⠀⠀⠀⠀⠐⢉⣯⠹⣀⣀⣢⡸⠉⢏⡄⣀⣯⠁ ⠀⠀⠀⠀⠡⠀⢹⣆⠀⠀⠀⣀⡀⡰⠀⢠⠖ ⠀⠀⠀⠀⠀⠈⠙⣿⣿⠀⠠⠚⢋⡁⠀⡜ ⠀⠀⠀⠀⠀⠀⢸⠈⠙⠦⣤⣀⣤⣤⡼⠁

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Answer 2

Step-by-step explanation:

let p(x) = x3-6x2+11x-6

by trial we find that

p(1)=(1)3-6(1)2 +11(1)-6=0

by converse of factor theorem, (x-1) is a factor of p(x)

now x3 -6x2+11x-6

=x2 (x-1)-5x(x-1)+6(x-1)

=(x-1){x2-2x-3x+6x}

=x-1{x(x-2)-3(x-2)}

=(x-1) (x-2(x-3)