26) Ta có: \(x^4-20x^2+64\)
\(=x^4-16x^2-4x^2+64\)
\(=x^2\left(x^2-16\right)-4\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-2\right)\left(x+2\right)\)
27) Ta có: \(4x^3+6x^2+3x+1\)
\(=4x^3+4x^2+2x^2+2x+x+1\)
\(=4x^2\left(x+1\right)+2x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(4x^2+2x+1\right)\)
28) Ta có: \(x^3-6x^2+12x-9\)
\(=x^3-3x^2-3x^2+9x+3x-9\)
\(=x^2\cdot\left(x-3\right)-3x\left(x-3\right)+3\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-3x+3\right)\)
29: Ta có: \(x^4+x^2+1\)
\(=x^4+2x^2+1-x^2\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\)
26) Ta có: x4−20x2+64x4−20x2+64
=x4−16x2−4x2+64=x4−16x2−4x2+64
=x2(x2−16)−4(x2−16)=x2(x2−16)−4(x2−16)
=(x−4)(x+4)(x−2)(x+2)=(x−4)(x+4)(x−2)(x+2)
27) Ta có: 4x3+6x2+3x+14x3+6x2+3x+1
=4x3+4x2+2x2+2x+x+1=4x3+4x2+2x2+2x+x+1
=4x2(x+1)+2x(x+1)+(x+1)=4x2(x+1)+2x(x+1)+(x+1)
=(x+1)(4x2+2x+1)=(x+1)(4x2+2x+1)
28) Ta có: x3−6x2+12x−9x3−6x2+12x−9
=x3−3x2−3x2+9x+3x−9=x3−3x2−3x2+9x+3x−9
=x2⋅(x−3)−3x(x−3)+3(x−3)=x2⋅(x−3)−3x(x−3)+3(x−3)
=(x−3)(x2−3x+3)=(x−3)(x2−3x+3)
29: Ta có: x4+x2+1x4+x2+1
=x4+2x2+1−x2=x4+2x2+1−x2
=(x2+1)2−x2=(x2+1)2−x2
=(x2−x+1)(x2+x+1)
