\(x^3+6x^2-13x-42\)

\(x^3+6x^2-13x-42\)

\(=\left(x+7\right)\left(x-3\right)\left(x+2\right)\)

b, \(2x^3-x^2+3x+6\)

\(=2x^3+2x^2-3x^2-3x+6x+6\)

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

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

\(x^3+6x^2-13x-42\)

\(=x^3+7x^2-x^2-7x-6x-42\)

\(=x^2\left(x+7\right)-x\left(x+7\right)-6\left(x+7\right)\)

\(=\left(x+7\right)\left(x^2-x-6\right)\)

\(=\left(x+7\right)\left(x-3\right)\left(x+2\right)\)

\(P\left(x\right)=6x^3+13x^2+4x-3\)

\(=\left(6x^3+6x^2\right)+\left(7x^2+7x\right)-\left(3x-3\right)\)

\(=6x^2\left(x+1\right)+7x\left(x+1\right)-3\left(x+1\right)\)

\(=\left(6x^2+7x-3\right)\left(x+1\right)\)

\(=\left[\left(6x^2-2x\right)+\left(9x-3\right)\right]\left(x+1\right)\)

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

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

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

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

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

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

\(=6x^2+3x+10x+5=3x\left(2x+1\right)+5\left(2x+1\right)=\left(3x+5\right)\left(2x+1\right)\)

6x2+3x+10x+5=3x(2x+1)+5(2x+1)=(3x+5)(2x+1)

=6x^2 - 4x - 9x +6

=(6x^2 -4x) - (9x-6)

=2x(3x -2) - 3(3x-2)

=(3x-2) (2x - 3)

giup e với

a) \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)

\(=\left[\left(x+8\right)-\left(x-2\right)\right]^2\)

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

\(=10^2\)

\(=2^2.5^2\)

b)\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

c)\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)

\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+5x+6\right)\)

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

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

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

d)\(x^3+6x^2-13x-42=x^3-3x^2+9x^2-27x+14x-42\)

\(=x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2+9x+14\right)\)

\(=\left(x-3\right)\left(x^2+2x+7x+14\right)\)

\(=\left(x-3\right)\left[x\left(x+2\right)+7\left(x+2\right)\right]\)

\(=\left(x-3\right)\left(x+2\right)\left(x+7\right)\)

\(x^4+6x^3+13x^2+12x+4\)

\(=x^4+x^3+5x^3+5x^2+8x^2+8x+4x+4\)

\(=x^3\left(x+1\right)+5x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3+5x^2+8x+4\right)\)

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

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

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

         \(6x^2+13x-15\)

\(=6x^2+18x-5x-15\)

\(=6x.\left(x+3\right)-5.\left(x+3\right)\)

\(=\left(x+3\right).\left(6x-5\right)\)

\(6x^2+13x-15\)

\(=6x^2+18x-5x-15\)

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

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

\(6x^2+13x-15\)

\(\Rightarrow6x^2+18x-5x-15x\)

\(\Rightarrow6x\times\left(x+3\right)-5\times\left(x+3\right)\)

\(\Rightarrow\left(x+3\right)\times\left(6x-5\right)\)

Code : Breacker

a) Ta có : 6x² - 13x + 6 = 6x² - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)

b) Ta có: 6x² + 7x - 3 = 6x² + 9x - 2x - 3 = 3x(2x + 3) - (2x + 3) = (3x - 1)(2x + 3)

\(a,6x^2-13x+6\)

\(=6x^2-9x-4x+6\)

\(=3x\cdot\left(2x-3\right)-x\cdot\left(2x-3\right)\)

\(=\left(2x-3\right)\cdot\left(3x-x\right)\)

\(=\left(2x-3\right)\cdot2x\)

\(b,6x^2+7x-3\)

\(=6x^2-2x+9x-3\)

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

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

\(a,6x^2-13x+6=6x^2-9x-4x+6\)

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

\(b,6x^2+7x-3=6x^2-2x+9x-3\)

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