Toán Lớp 8: Phân tích đa thức thành nhân tử:
$a,$ $x^{4}$ $-$ $x^{2}$ $+$ $x$ $-$ $1$
$b,$ $2x^{2}$ $-$ $5x$ $-$ $3$
$c,$ $3x^{2}$ $-$ $5x$ $-$ $2$
$d,$ $x^{3}$ $+$ $2x$ $-$ $3$
$e,$ $x^{4}$ $-$ $9x^{3}$ $+$ $28x^{2}$ $-$ $36x$ $+$ $16$
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$=x^2(x^2-1)+(x-1)$
$=(x-1)(x^3+x^2+1)$
b,
$=2x^2-6x+x-3$
$=2x(x-3)+(x-3)$
$=(x-3)(2x+1)$
c,
$=3x^2-6x+x-2$
$=3x(x-2)+(x-2)$
$=(x-2)(3x+1)$
d,
$x^3+2x-3$
$=x^3-x^2+x^2-x+3x-3$
$=x^2(x-1)+x(x-1)+3(x-1)$
$=(x^2+x+3)(x-1)$
e,
$=x^4-x^3-8x^3+8x^2+20x^2-20x-16x+16$
$=x^3(x-1)-8x^2(x-1)+20x(x-1)-16(x-1)$
$=(x-1)(x^3-8x^2+20x-16)$
$=(x-1)(x^3-2x^2-6x^2+12x+8x-16)$
$=(x-1)[x^2(x-2)-6x(x-2)+8(x-2)]$
$=(x-1)(x-2)(x^2-6x+8)$
$=(x-1)(x-2)[x(x-2)-4(x-2)]$
$=(x-1)(x-2)^2(x-4)$