a) Ta có: \(x^4+3x^3-7x^2-27x-18\)
\(=x^4-3x^3+6x^3-18x^2+11x^2-33x+6x-18\)
\(=x^3\left(x-3\right)+6x^2\left(x-3\right)+11x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(x^3+6x^2+11x+6\right)\)
\(=\left(x-3\right)\left(x^3+x^2+5x^2+5x+6x+6\right)\)
\(=\left(x-3\right)\left[x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\right]\)
\(=\left(x-3\right)\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b) Ta có: \(x^3-8x^2+x+42\)
\(=x^3-7x^2-x^2+7x-6x+42\)
\(=x^2\left(x-7\right)-x\left(x-7\right)-6\left(x-7\right)\)
\(=\left(x-7\right)\left(x^2-x-6\right)\)
\(=\left(x-7\right)\left(x-3\right)\left(x+2\right)\)
c) Ta có: \(x^4+5x^3-7x^2-41x-30\)
\(=x^4+5x^3-7x^2-35x-6x-30\)
\(=x^3\left(x+5\right)-7x\left(x+5\right)-6\left(x+5\right)\)
\(=\left(x+5\right)\left(x^3-7x-6\right)\)
\(=\left(x+5\right)\left(x^3-x-6x-6\right)\)
\(=\left(x+5\right)\left[x\left(x^2-1\right)-6\left(x+1\right)\right]\)
\(=\left(x+5\right)\left[x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\right]\)
\(=\left(x+5\right)\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+5\right)\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
a ) \(==>x^3.\left(x+3\right)-\left(7x^2+27x+18\right)\)
ko xét phần x^3.( x+3 ) nữa mà mik phân tích trong ngoặc nha zo thi ko lm như vậy mà ghi lại phần đó nha
\(7x^2+21x+6x+18\)
\(7x\left(x+3\right)+6\left(x+3\right)\)
\(\left(x+3\right)\left(7x+6\right)\)
==> \(x^3.\left(x+3\right)-\left(x+3\right)\left(7x+6\right)\)
==>\(\left(x+3\right)\left(x^3-7x-6\right)\)
