Phân tích đa thức thành nhân tử
a) 4x2-36x+56 = 4\(x^2\)-36x+81-25 = \(\left(2x\right)^2\)-2.2x.9+\(9^2\) - 25 = \(\left(2x-9\right)^2\)-\(5^2\) = ( 2x - 9 - 5 ).( 2x - 9 + 5 ) = ( 2x - 14 ).( 2x - 4 )
b ) x4+4x2 = \(x^2.\left(x^2+4\right)\)
c ) x4 + x2 +1 = \(x^2\left(x^2+2\right)\)
d) 64\(x^4+1\)=\(64\left(x^4+1\right)\)
e ) 81x4+1=\(81\left(x^4+1\right)\)
a, 4x2 - 36x + 56
= (4x2 - 36x + 81) - 25
= (2x - 9) - 52
= (2x - 9 - 5).(2x - 9 + 5)
= (2x - 14).(2x - 4)
= 2 (x - 7).2 (x - 2)
= 4 (x - 7) (x - 2)
b, x4 - 4x2
= x2 (x2 - 4)
= x2 (x - 2) (x + 2)
c, x4 + x2 + 1
= x4 + x2 + 1 + x2 - x2
= (x4 + x2 + x2 + 1) - x2
= (x4 + 2x2 + 1) - x2
= (x2 + 1)2 - x2
= (x2 + 1 - x) (x2 + 1 + x)
d, 64x4 + 1
=
