\(a.A=\left(x^4-3x^3\right)+\left(-8x^3+24x^2\right)+\left(2x^2-6x\right)+\left(-16x+48\right)\\ =x^3\left(x-3\right)-8x^2\left(x-3\right)+2x\left(x-3\right)-16\left(x-3\right)\\ =\left(x-3\right)\left(x^3-8x^2+2x-16\right)\\ =\left(x-3\right)\left[x^2\left(x-8\right)+2\left(x-8\right)\right]\\ =\left(x-3\right)\left(x^2+2\right)\left(x-8\right)\\ b.B=x^5+3x^4+x^3-11x^2-30x-20\\ =\left(x^5+x^4\right)+\left(2x^4+2x^3\right)+\left(-x^3-x^2\right)+\left(-10x^2-10x\right)+\left(-20x-20\right)\\ =x^4\left(x+1\right)+2x^3\left(x+1\right)-x^2\left(x+1\right)-10x\left(x+1\right)-20\left(x+1\right)\\ =\left(x+1\right)\left(x^4+2x^3-x^2-10x-20\right)\\ =\left(x+1\right)\left[\left(x^4-5x^2\right)+\left(2x^3-10x^2\right)+\left(4x^2-20\right)\right]\\ =\left(x+1\right)\left[x^2\left(x^2-5\right)+2x\left(x^2-5\right)+4\left(x^2-5\right)\right]\\ =\left(x+1\right)\left(x^2-5\right)\left(x^2+2x+4\right)\)
a) `A=x^4-11x^3+26x^2-22x+48`
`=(x^4+2x^2)-(11x^3+22x)+(24x^2+48)`
`=x^2(x^2+2)-11x(x^2+2)+24(x^2+2)`
`=(x^2+2)(x^2-11x+24)`
`=(x^2+2)(x^2-3x-8x+24)`
`=(x^2+2)[x(x-3)-8(x-3)]`
`=(x^2+2)(x-3)(x-8)`
b) `B=x^5+3x^4+x^3-11x^2-30x-20`
`=(x^5+x^4)+(2x^4+2x^3)-(x^3+x^2)-(10x^2+10x)-(20x+20)`
`=x^4(x+1)+2x^3(x+1)-x^2(x+1)-10x(x+1)-20(x+1)`
`=(x+1)(x^4+2x^3-x^2-10x-20)`
`=(x+1)(x^4-5x^2+2x^3-10x+4x^2-20)`
`=(x+1)[x^2(x^2-5)+2x(x^2-5)+4(x^2-5)]`
`=(x+1)(x^2-5)(x^2+2x+4)`
#$\mathtt{Toru}$
a) $A = (x^{4} - 3x^{3}) + (-8x^{3} + 24x^{2}) + (2x^{2} - 6x) + (-16x + 48)$
$= x^{3}(x - 3) - 8x^{2}(x - 3) + 2x(x - 3) - 16(x - 3)$
$= (x - 3)(x^{3} - 8x^{2} + 2x - 16)$
$= (x - 3)[x^{2}(x - 8) + 2(x - 8)]$
$= (x - 3)(x^{2} + 2)(x - 8)$
b) $B = x^{5} + 3x^{4} + x^{3} - 11x^{2} - 30x - 20$
$= (x^{5} + x^{4}) + (2x^{4} + 2x^{3}) + (-x^{3} - x^{2}) + (-10x^{2} - 10x) + (-20x - 20)$
$= (x + 1)(x^{4} + 2x^{3} - x^{2} - 10x - 20) - 20(x + 1)$
$= (x + 1)[(x^{4} - 5x^{2}) + (2x^{3} - 10x^{2}) + (4x^{2} - 20)]$
$= (x + 1)[x^{2}(x^{2} - 5) + 2x(x^{2} - 5) + 4(x^{2} - 5)]$
$= (x + 1)(x^{2} - 5)(x^{2} + 2x + 4)$
$#haeng2010$
