Đáp án:
Giải thích các bước giải:
`a, (x²+x)²-14(x²+x)+24`
Đặt : `(x²+x) = t `
`⇒ t²-14t+24`
`= t²-2t-12t+24`
`= t(t-2)-12(t-2)`
`= (t-2)(t-12)`
Thay `t = (x²+x)`
`⇒ (x²+x-2)(x²+x-12)`
_________
`c. x^4+2x³+5x²+4x-12`
`= (x^4 - x³) +(3x³ - 3x²) +(8x²-8x)+(12x-12) `
`= x³(x-1)+3x²(x-1)+8x(x-1)+12(x-1)`
`= (x-1)(x³+3x²+8x+12)`
`= (x-1)[(x³+2x²)+(x²+2x)+(6x+12)]`
`= (x-1)[x²(x+2)+x(x+2)+6(x+2)]`
`= (x-1)(x+2)(x²+x+6)`
__________
`e. (x+1)(x+3)(x+5)(x+7)+15`
`=[(x+1)(x+7)][(x+3)(x+5)] +15`
`= (x²+7x+x+7)(x²+5x+3x+15)+15`
`= (x²+8x+7)(x²+8x+15)+15`
Đặt `(x²+8x+11) = y `
`= (y-4)(y+4)+15`
`= (y²-4²)+15`
`= y²-16+15`
`= y²-1`
`= (y-1)(y+1)`
`= (x²+8x+11-1)(x²+8x+11+1)`
`= (x²+8x+10)(x²+8x+12)`
