Question

Phân tích đa thức thành nhân tử

a) x³ +x+2

b) x³-2x-1

c) x³+3x²-4

d) x³+3x²y-9xy²+5y³

Answer 1

a) x³ +x+2

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

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

b) x³-2x-1

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

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

c) x³+3x²-4

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

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

d) x³+3x²y-9xy²+5y³

=\(\left(x^3-x^2y\right)+\left(4x^2y-4xy^2\right)-\left(5xy^2-5y^3\right)\)

=\(\left(x-y\right)\left(x^2+4xy-5y^2\right)\)

=\(\left(x-y\right)^2\left(x-5y\right)\)

Answer 2

a)

\(x^3+x+2\)

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

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

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

b)

\(x^3-2x-1\)

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

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

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

c)

\(x^3-3x^2-4\)

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

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

\(=\left(x-1\right)\left(x^2+2.2.x+2^2\right)\)

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

d)

\(x^3-3x^2y-9xy^2+5y^3\)

\(=\left(x^3-x^2y\right)+\left(4x^2y-4xy^2\right)-\left(5xy^2-5y^3\right)\)

\(=x^2\left(x-y\right)+4xy\left(x-y\right)-5y^2\left(x-y\right)\)

\(=\left(x-y\right)\left(x^2-4xy-5y^2\right)\)

\(=\left(x-y\right)^2\left(x-5y\right)\)