Exercice 1 --- (id : 1258)
Activités algébriques: Exercice 1
correction
1) A=9x212x+4+x3+3x2+3x+1A=9{x}^{2}−12x+4+{x}^{3}+{3x}^{2}+3x+1
 \Leftrightarrow A=12x29x+5+x3A=12{x}^2{}−9x+5+{x}^{3}
\Leftrightarrow A=x3+12x29x+5A={x}^{3}+12{x}^{2}−9x+5
2) B=x(3x1)+(3x1)2B=x(3x−1)+(3x-1)^{2}
\Leftrightarrow B=(3x1)(x+3x1)B=(3x−1)(x+3x−1)
\Leftrightarrow B=(3x1)(4x1)B=(3x−1)(4x−1)
C=43x353C={4}^{3}{x}^{3}−{5}^{3}
\Leftrightarrow C=(4x)353C=(4x)^{3}−{5}^{3}
\Leftrightarrow C=(4x5)((4x)2+4x×5+52)C=(4x−5)((4x)^{2}+4x×5+{5}^{2})
\Leftrightarrow C=(4x5)(16x2+20x+25)C=(4x−5)(16{x}^{2}+20x+25)