Question

Phân tích đa thức thành nhân tử:

a) 2x^3 - 35x +75

b) x^6 -9x^3 +8

c) x^5 +x^4 +x^3 + x^2 +x +1

d) 3x^3 -4x^2 +13x -4

Answer 1

\(2x^3-35x+75=2x^2\left(x+5\right)-10x\left(x+5\right)+15\left(x+5\right)=\left(x-5\right)\left(2x^2-10+15\right) \)

Answer 2

c/ \(x^5+x^4+x^3+x^2+x+1\)

= \(\left(x^5+x^4\right)+\left(x^3+x^2\right)+\left(x+1\right)\)

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

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

Answer 3

\(x^6-9x^3+8\)

\(=x^2\left(x^4-2x^3-x+2\right)+2x\left(x^4-2x^3-x+2\right)+4\left(x^4-2x^3-x+2\right)\)

\(=\left(x^4-2x^3-x+2\right)\left(x^2+2x+4\right)\)

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

\(=\left(x-2\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2+2x+4\right)\)

Answer 4

\(2x^3-35x+75\)

\(=2x^3-50x+15x +75\)

\(=2x\left(x^2-25\right)+15\left(x+5\right)\)

\(=2x\left(x-5\right)\left(x+5\right)+15\left(x+5\right)\)

\(=\left(x+5\right)\left(2x^2-10x+15\right)\)

== clgt