Question

phan tich cac da thuc sau thanh nhan tu

x^2-x-12

x^2+8x+15

x^3-x^2+x+3

x^8+3x^4+4

x^6-x^4-2x^3+2x^2

Answer 1

c)\(x^3-x^2+x+3=x^2+x-2x^2-2x+3x+3\)

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

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

d)\(x^8+3x^4+4=\left(x^8+4x^4+4\right)-x^4=\left(x^4+2\right)^2-\left(x^2\right)^2\)

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

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

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

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

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

Answer 2

a)\(x^2-x-12\)

\(=x^2+4x-3x-12\)

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

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

b) \(x^2+8x+15\)

\(=x^2+3x+5x+15\)

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

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