=x(x^3+7x^2+14x+14+4)

=x(x^3+7x^2+14x+18)

   x⁴+7x³+14x²+14x+4

=x⁴+7x³+4x²+10x²+14x+4

=(x⁴+4x²+4)+(7x³+14x)+10x²

=(x²+2)²+7x(x²+2)+10x²

=(x²+2)²+2x(x²+2)+5x(x²+2)+10x²

=(x²+2)(x²+2+2x)+5x(x²+2+2x)

=(x²+2+2x)(x²+2+5x)

\(x^4+7x^3+14x^2+14x+4\)

\(=x^4+x^3+6x^3+6x^2+8x^2+8x+4x+4\)

\(=x^3\left(x+1\right)+6x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3+6x^2+8x+4\right)\)

\(x^4-14x^2-7x+30=\left(x^4+x^3-3x^2\right)+\left(-x^3-x^2+3x\right)+\left(-10x^2-10x+30\right)\)

\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-10\left(x^2+x-3\right)\)

\(=\left(x^2+x-3\right)\left(x^2-x-10\right)\)

x^4-14*x^2-7*x+30=(x^2-x-10)*(x^2+x-3)

b) 3x⁴-3x³+9x³-9x²-24x²+24x-48x+48

=3x³(x-1)+9x²(x-1)-24x(x-1)-48(x-1)

=(x-1)(3x³+9x²-24x-48)

=3(x-1)(x³+3x²-8x-16)

\(x^4-14x^2-7x+30\)

\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-10\left(x^2+x-3\right)\)

\(=\left(x^2+x-3\right)\left(x^2-x-10\right)\)

Nhớ chọn cho tớ nhe!

Lời giải:
a. $x^3-4x^2+x+6=(x^3-2x^2)-(2x^2-4x)-(3x-6)$

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

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

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b.

$x^3+7x^2+14x+8=(x^3+x^2)+(6x^2+6x)+(8x+8)$

$=x^2(x+1)+6x(x+1)+8(x+1)=(x+1)(x^2+6x+8)$

$=(x+1)[(x^2+2x)+(4x+8)]=(x+1)[x(x+2)+4(x+2)]$

$=(x+1)(x+2)(x+4)$