Question

hort Answer Type
Find the number of factors for the polynomial
f(x) = x9- X​

Answer 1

Answer:

ᴛʜᴇʀᴇ ᴀʀᴇ 5 ꜰᴀᴄᴛᴏʀꜱ ᴏꜰ ꜰ(x)⇒(x),(x4+1),(x2+1),(x−1) ᴀɴᴅ (x+1)

Step-by-step explanation:

ꜰ(x)=x 9−x

=x(x 8 −1)

=x[(x 4 ) 2 −(1) 2 ]

=x[(x 4 −1)(x 4 +1)]

=x(x 4+1)[(x 2 ) 2 −1 2 ]

=x(x 4 +1)(x 2 +1)(x 2−1)

=x(x 4 +1)(x 2 +1)(x−1)(x+1)

∴ ᴛʜᴇʀᴇ ᴀʀᴇ 5 ꜰᴀᴄᴛᴏʀꜱ ᴏꜰ ꜰ(x)⇒(x),(x 4 +1),(x2+1),(x−1) ᴀɴᴅ (x+1)

ᎻϴᏢᎬ ᎷᎽ ᎪΝՏᏔᎬᎡ ᏆՏ ᎻᎬᏞᏢҒႮᏞ ҒϴᎡ ᎽϴႮ (◕ᴗ◕✿)