Question

phân tích các đa thức sau thành nhân tử

a) \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)    

b) \(\left(x^2+2x\right)^2+9x^2+18x+20\)

Answer 1

      \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)

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

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

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

      \(\left(x^2+2x\right)^2+9x^2+18x+20\)

\(=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\)

\(=\left(x^2+2x\right)^2+5\left(x^2+2x\right)+4\left(x^2+2x\right)+20\)

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

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

Answer 2

a, \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)

Gọi \(x^2+x=A\)

\(\Rightarrow A^2-2A-15\)

\(\Rightarrow\left(A-3\right)\left(A+5\right)\)

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

Answer 3

lm nhầm :

\(\Rightarrow\left(A+3\right)\left(A-5\right)\)

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

Answer 4

\(b,\left(x^2+2x\right)^2+9x^2+18x+20\)

\(=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\)

gọi \(\left(x^2+2x\right)^2=A\)

\(\Rightarrow A^2+9A+20\Rightarrow A^2+4A+5A+20\)

\(\Rightarrow A\left(A+4\right)+5\left(A+4\right)\Rightarrow\left(A+5\right)\left(A+4\right)\)

thay A = ( x²  + 2x) 

\(\Rightarrow\left(x^2+2x+5\right)\left(x^2+2x+4\right)\)