Question

phân tích đa thức thành nhân tử

x^3-7x+6

x^3-9x^2+6x+16

Answer 1

a) x^3 - 7x - 6

= x^3 - x - 6x - 6

= x(x^2 - 1 ) - 6 (x + 1 )

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

= ( x+ 1 ) [ x(x-1) - 6 ]

= ( x + 1 )(x^2 - x - 6 )

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

= ( x+ 1 ) [ x(x-3) + 2 ( x- 3 )]

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

Answer 2

\(x^3-9x^2+6x+16\)

\(=x^3+x^2-10x^2-10x+16x+16\)

\(=(x^3+x^2)-(10x^2+10x)+(16x+16)\)

\(=x^2(x+1)-10x(x+1)+16(x+1)\)

\(=(x+1)(x^2-10x+16)\)

\(=(x+1)(x^2-2x-8x+16)\)

\(=(x+1)[(x^2-2x)-(8x-16)]\)

\(=(x+1)[x(x-2)-8(x-2)]\)

\(=(x+1)(x-2)(x-8)\)