Question

Bài 1 : Phân tích đa thức thành nhân tử :

a) 2x^4+5x^3+13x^2+25x+15

b) x^4+3x^3+x^2-12x-20

c) (a+b)^3-(a-b)^3)

d) x^3+y^3+z^3-3xyz

e) a*(a+2b)^3-b*(2a+b)^3

f) x-19x-30

g) a*(b+c)^2*(b-c)+b*(c+a)^2*(c-a)+c*(a+b)^2*(a-b)

Answer 1

a: \(=2x^4+2x^3+3x^3+3x^2+10x^2+10x+15x+15\)

\(=\left(x+1\right)\left(2x^3+3x^2+10x+15\right)\)

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

b: \(x^4+3x^3+x^2-12x-20\)

\(=x^4-2x^3+5x^3-10x^2+11x^2-22x+10x-20\)

\(=\left(x-2\right)\left(x^3+5x^2+11x+10\right)\)

\(=\left(x-2\right)\left(x^3+2x^2+3x^2+6x+5x+10\right)\)

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

c: \(=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

\(=2b\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)

\(=2b\left(3a^2+b^2\right)\)

d: \(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2\right)-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

f: \(x^3-19x-30\)

\(=x^3-5x^2+5x^2-25x+6x-30\)

\(=\left(x-5\right)\left(x^2+5x+6\right)\)

\(=\left(x-5\right)\left(x+2\right)\left(x+3\right)\)